The Estudios empirical de Economía. foundation Vol. of 28 the - golden Nº 1, Junio rule / 21. Víctor Págs. J. Elías 79-88 79 THE EMPIRICAL FOUNDATION OF THE GOLDEN RULE VÍCTOR J. ELÍAS* Abstract This working paper analizes with cross-sectional data if the Golden Rule condition satisfies: where the saving index is equal to capital (β) or to the real interest rate, equal to the gross output growth of households. Resumen Este paper analiza con datos de corte transversal si se cumple la condición de la Regla de Oro: donde el índice de ahorro es igual al capital (β), o el tipo de interés real (i), igual al crecimiento bruto del producto de los hogares. Se analizarán las implicancias que podría tener ésta, para la pérdida de eficacia o bienestar. JEL: E6, E1, 11, 2. Keywords: Development, efficiency, welfare. I. INTRODUCTION The Golden Rule (GR) as developed by E. Phelps (1966) gives the condition under which a country will grow maximizing its consumption per capita. The condition is obtained when the country is growing in its long run path with stability fulfilled. * I appreciate the comments of Professor Ricardo Caballero about the existence of a very interesting literature on the empirical assessment about dynamic efficiency specially the work of Abel-Mankiw-Summers-Zeckhauser (1989) where they use as criteria the comparison of total profits with total investment. Dynamic efficiency exist if profits are greater than investment for a reasonable long period. They suggest that this criteria is much better than to use the golden rule criteria. I will work also on this line than in some respects could be similar. My impression is that we should work much more on this empirical avenue. The suggestions of R. Cifuentes and the ones coming out from the conference were also very useful. University of Tucuman and Foundation Banco Empresario.
8 Estudios de Economía, Vol. 28 - Nº 1 The objective of this paper is to check with cross-country data if this condition provided by the GR: rate of saving (s) equal to the capital share (β), or real interest rate (i) equal to gross domestics product growth (GDP), are actually fulfilled. Even though these are long-run conditions could be of interest to analyze how far are they from current conditions, and what are the implications for efficiency or welfare loss. This very preliminar exercise will use the data provided by the World Development Indicators 2 (World Bank) and other studies that provides estimates of β, capital growth and Total Factor Productivity (TFP). For some of the parameters there are information for almost countries, but much less of 1 of them covers all the relevant parameters. II. DATA BEHAVIOR In this section we present frequency distributions for real interest rate (i); annual GDP rate of growth for the period 196-1998 (y); capital share (β 1 ); share of total income of the upper 1th decile group (β 2 ); annual capital stock rate of growth for the period 19-1987 (k); annual Total Factor Productivity rate of growth for the period 19-1987 (g); acceleration of the rate of change of the GDP ( y) between the 9 s with respect to the 8 s. FIGURE A FREQUENCY OF DISTRIBUTION OF THE VARIABLES AND PARAMETERS A.1. Frequency Distribution of Real Rate Interest 1998 (i) 2 A.2. Frequency Distribution of GDP Rate of Change 6-98 (y) 14 2 1 12 1 8 6 4 2-2. -12.. 12. 2. 37.. Real Rate of Interest -4-2 2 4 6 8 1 GDP Rate of Change
The empirical foundation of the golden rule / Víctor J. Elías 81 FIGURE A (cont.) FREQUENCY OF DISTRIBUTION OF THE VARIABLES AND PARAMETERS A.3. Frequency Distribution of GDP Rate of Change 9-98 GDP Rate of Change 8-9 ( y) 2 A.4. Frequency Distribution of Gross Domestic Saving 198 (s 8 ) 2 2 2 1 1-16 -14-12 -1-8 -6-4 -2 2 4 6 8 GDP Rate of Change 9-98 GDP Rate of Change 8-9 -6-4 -2 2 4 6 Gross Domestic Saving A.. Frequency Distribution of Gross Domestic Saving 198 (s 98 ) A.6. Frequency Distribution of Capital Share (β 1 ) 2 8 2 6 4 1 2-37. -2. -12.. 12. 2. 37.. 2 3 4 6 7 8 9 Gross Domestic Saving Capital Share
82 Estudios de Economía, Vol. 28 - Nº 1 FIGURE A (cont.) FREQUENCY OF DISTRIBUTION OF THE VARIABLES AND PARAMETERS A.7. Frequency Distribution of Share of Income of Top 1% (β 1 ) A.8. Frequency Distribution of GDP per capita 1998 (GDP/N) 12 2 1 8 6 4 2 2 1 18 2 22 24 26 28 3 32 34 36 38 4 42 44 46 48 Share of Income of Top 1% 4 8 12 16 2 24 28 GDP per capita A.9. Frequency Distribution of Change of TFP 19-87 (g) A.1. Frequency Distribution of Capital Rate of Growth 19-87 (k) 1 12 8 1 6 4 2 8 6 4 2-3 -2-1 1 2 3 4 Change of TFP -2.. 2.. 7. 1. 12.. Capital Rate of Growth
The empirical foundation of the golden rule / Víctor J. Elías 83 TABLE Nº 1 SUMMARY OF THE BEHAVIOR OF MAIN VARIABLES AND PARAMETERS Standard Number Parameters Mean Deviation of Observations i Real rate of interest (1998) 1. 12.7 y GDP rate of change 6-98 2.1 2.4 11 y GDP rate of change 9-98 GDP rate of change 8-9.2 4.1 144 s 8 Gross domestic saving 198 19.7 17.1 113 S 98.1 13.3 136 β 1 Capital share (near 1998) 1. 18.6 81 β 2 Share of income of top 1% (near 1998) 31.1 7.6 18 Y/N GDP per capita 1998 6944.8 733.8 13 g Change of TFP (19-1987) 1.1 1.4 92 k Capita rate of growth (19-1987) 4.8 3. 92 III. GOLDEN RULE S VERIFICATION In this section we verify how close is satisfied the GR. We make the following graphical analysis: 1. How far are the countries from their long run conditions: we compare GDP Growth (y) with the Capital Growth (k): Capital rate of growth (19-1987) 2 1 R 2 =.34 k*.7. y* - - 1 2 GDP rate of change 6-98
84 Estudios de Economía, Vol. 28 - Nº 1 2. How far are the countries from the GR s condition i = y (*): 6 Real rate of interest (1998) 4 2-2 -4-1 2 GDP rate of change 6-98 6 Real rate of interest (1998) 4 2-2 -4-1 2 GDP rate of change 6-98 Lower GDP per capita 6 4 Real rate of interest (1998) 2-2 -4-1 2 GDP rate of change 6-98 Upper GDP per capita (*) Milton Friedman (1971) in some of his estimates of demand function for money used y as a proxy for i, based on this GR.
The empirical foundation of the golden rule / Víctor J. Elías 8 3. How far are the countries from GR s s = β: 1 4 8 6 4 2-2 -4-6 -6-4 -2 2 4 6 8 1 Capital share (near 1998) 1 8 6 4 2-2 -4-6 -6-4 -2 2 4 6 8 1 Capital share (near 1998) Lower GDP per capita 1 8 6 4 2-2 -4-6 -6-4 -2 2 4 6 8 1 Capital share (near 1998) Upper GDP per capita
86 Estudios de Economía, Vol. 28 - Nº 1 6 4 2-2 -4-6 -6-4 -2 2 4 6 Share of income of top 1% (near 1998) 6 4 2-2 -4-6 -6-4 -2 2 4 6 Share of income of top 1% (near 1998) Lower GDP per capita 6 4 2-2 -4-6 -6-4 -2 2 4 6 Share of income of top 1% (near 1998) Upper GDP per capita
The empirical foundation of the golden rule / Víctor J. Elías 87 IV. SOME IMPLICATIONS As we do no get a verification of the GR s we try to see if the departure from it could be explained by: 1. If the two GR s are consistent: 4 GDP rate of change Real rate of interest 2-2 -4-6 -1-8 -6-4 -2 2 Gross domestic saving Capital share 2. If the departure of s from b are related to efficiency problems. We relate s β with TFP growth: 2 Gross domestic saving Capital share -2-4 -6-8 -1-4 -2 2 4 Change of TFP (19-1987)
88 Estudios de Economía, Vol. 28 - Nº 1 Real rate interest GDP rate of change 6 4 2-2 -4-4 -2 2 4 Change of TFP (19-1987) V. REFERENCES 1. Abel, Andrew, N.G. Mankiw, L. Summers and R. Zeckhauser (1989). Assessing Dynamic Efficiency: Theory and Evidence, Review of Economic Studies, 6, pp. 1-2. 2. Elías, Víctor (1993). The Role of Total Factor Productivity on Economic Growth, Estudios de Economía, Volume 2, Special Number, June. 3. Friedman, Milton (March-April 1971). A Monetary Theory of Nominal Income, Journal of Political Economy, 79, pp. 323-37. 4. Gollin, Douglas (1998). Getting Income Shares Right: Self-Employment, Unincorporated Enterprise, and the Cobb-Douglas Hypothesis, draft, Williams College, Williamstown, Department of Economics.. Phelps, Edmund (1966). Golden Rules of Economic Growth, New York, Norton. 6. The World Bank (2), World Development Indicators World Bank 2, Washington D.C.