UIUC Econ303 Section I Growth theory Chapter 7c 8 Growth accounting and convergence Study economic growth using statistics growth accounting Production function z is TFP calculated as Solow residual is capital share Impact of each factor on output derivatives Intermediate Macro Zhao 1 UIUC Econ303 Growth accounting of GDP Total impact Contribution of each factors Capital Labor TFP US economy with production function Year GDP billions 2005 Capital billions 2005 Labor millions 1950 2159 3 7421 4 58 89 8 59 2000 Growth TFP 11216 4 36999 0 136 90 15 27 3 35 3 21 1 70 1 16 28 75 35 52 31 64 Contribution 100 Solow residual Annual average growth rate Contribution Intermediate Macro Zhao 2 UIUC Econ303 Growth Accounting page 26 Growth accounting for living standard aka GDP per capita GDP per capita TFP Capital per worker of population that are working ALP derivation Growth accounting Intermediate Macro Zhao 3 UIUC Econ303 Growth accounting page 27 for GDP per capita Growth accounting for South Korea Intermediate Macro Zhao GDP GDP per capita Growth rate 9 43 7 7 Contribution of labor 16 61 9 1 Contribution of capital 43 09 41 8 Contribution of technology 39 02 47 8 4 UIUC Econ303 Explain income differences development accounting From production function TFP GDP per capita Capital per worker of population that are working From data Country Population thousands GDP per capita 1985 Capital per worker 1985 Labor force as of population Total Factor productivity 1965 US India 194 309 487 337 11 649 17 507 42 918 751 786 42 174 1990 US India 250 372 849 515 18 054 34 705 49 947 1 264 1 946 39 228 Two engines of growth Intermediate Macro Zhao 1 Capital accumulation investment 2 TFP growth human capital accumulation technology progress others 5 UIUC Econ303 Growth rate and initial position Convergence and divergence A rich country grows slower than a poor country Income difference shrinks Intermediate Macro Zhao A rich country grows faster than a poor country Income difference expands 6 UIUC Econ303 Steady state comparisons only explain income differences A country is richer higher GDP per capita if its investment rate is higher its population growth rate is lower its TFP is higher At the steady state the growth rate is zero To explain growth we need to look at dynamics before reaching steady state Dynamics before reaching steady state Depreciation and diluting Investment net increase k0 Intermediate Macro Zhao k1 k2 k3 k 7 UIUC Econ303 Track the movement of capital A sample economy TFP Capital share Saving rate Depreciation Population growth Starting point Output in 1965 Capital increase in 1965 Capital in 1966 Tracking capital overtime page 28 Intermediate Macro Zhao 8 UIUC Econ303 Let s break it down General formula Parameter values Formula for this problem Time period Diminishing marginal product catching up convergence Real GDP per worker C A Intermediate Macro Zhao 8 000 17 000 UK Poor grows fast US Rich grows slowly Physical capital per worker 9 UIUC Econ303 Math Appendix the growth rate Growth rate of capital per capita Growth rate of GDP per capita Studies on regions of Europe Intermediate Macro Zhao 10 UIUC Econ303 Barro and Sala i Martin Brookings papers and proceedings 1991 Intermediate Macro Zhao 11 UIUC Econ303 Negative correlation between initial capital and growth rate does not hold for a broader set of countries Conditional Convergence page 29 Intermediate Macro Zhao 12 UIUC Econ303 Comparing US and India Country US India Investment rate s 21 5 13 8 Population growth rate n 1 09 2 26 947 228 Capital intensity now 17000 800 Subsequent growth of y 9 06 10 Steady state 170632 7837 TFP z Conditional Convergence Intermediate Macro Zhao 13 UIUC Econ303 Conditional convergence The absolute convergence holds if all countries are alike Over time all countries converges to the same steady state 50 states within the US and prefectures within Japan A group of Western European countries In reality countries differ In particular countries have different productivity investment rate and population growth rate Countries with lower productivity and lower saving rate and higher population growth are permanently poor Lower steady state The growth rate is higher only when a country is far from its steady state Intermediate Macro Zhao 14
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