1Intermediate Macro ZhaoUIUC Econ303Section I: Growth theoryChapter 7c, 8: Growth accounting and convergenceStudy economic growth using statistics – growth accounting.• Production function– z is TFP calculated as Solow residual– α is capital share• Impact of each factor on output – derivatives2Intermediate Macro ZhaoUIUC Econ303Growth accounting of GDP• Total impact• Contribution of each factorsCapitalLaborTFPUS economy with production function Ye ar G DP (billions 2005 $)Capital(billions, 2005 $)Labor(millions)TFP1950 2159.3 7421.4 58.892000 11216.4 36999.0 136.90GrowthContribution 100%8.5915.273.35% 3.21% 1.70% 1.16%28.75% 35.52% 31.64%Solow residualAnnual average growth rate Contribution3Intermediate Macro ZhaoUIUC Econ303Growth Accounting (page 26)Growth accounting for living standard, aka GDP per capitaGDP per capitaTFPCapital per worker% of population that are workingALPderivationGrowth accounting4Intermediate Macro ZhaoUIUC Econ303Growth accounting (page 27) for GDP per capitaGrowth accounting for South KoreaGDPGDP per capitaGrowth 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%5Intermediate Macro ZhaoUIUC Econ303Explain income differences – development accounting• From production function •From dataGDP per capitaTFPCapital per worker% of population that are workingCountry US India US IndiaPopulation (thousands) 194,309 487,337 250,372 849,515GDP per capita (1985 $) 11,649 751 18,054 1,264Capital per worker ( 1985 $) 17,507 786 34,705 1,946Labor force as % of population 42% 42% 49% 39%Total Factor productivity 918 174 947 2281965 1990Two engines of growth1. Capital accumulation -- investment2. TFP growth – human capital accumulation, technology progress, others6Intermediate Macro ZhaoUIUC Econ303Growth rate and initial position Convergence and divergenceA rich country grows slower than a poor countryIncome difference shrinksA rich country grows fasterthan a poor countryIncome difference expands7Intermediate Macro ZhaoUIUC Econ303Steady 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 statekDepreciation and dilutingInvestmentk0net increasek1k2k38Intermediate Macro ZhaoUIUC Econ303Track 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 1966Tracking capital overtime (page 28)9Intermediate Macro ZhaoUIUC Econ303• General formula• Parameter values • Formula for this problem• Time periodLet’s break it downDiminishing marginal product, catching-up, convergenceReal GDP per worker$8,000 17,000Physical capital per worker ACUSRich, grows slowlyUKPoor, grows fast10Intermediate Macro ZhaoUIUC Econ303Math Appendix: the growth rate• Growth rate of capital per capita • Growth rate of GDP per capita Studies on regions of Europe11Intermediate Macro ZhaoUIUC Econ303Barro and Sala-i-Martin Brookings papers and proceedings (1991)12Intermediate Macro ZhaoUIUC Econ303Negative correlation between initial capital and growth rate does not hold for a broader set of countries.Conditional Convergence (page 29)13Intermediate Macro ZhaoUIUC Econ303Comparing US and IndiaCountry US IndiaInvestment rate, s 21.5% 13.8%Population growth rate, n 1.09% 2.26%TFP, z 947 228Capital intensity now 17000 800Subsequent growth of y 9.06% 10%Steady state 170632 7837Conditional Convergence14Intermediate Macro ZhaoUIUC Econ303Conditional 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
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