Ch1_Solow Growth.hwp

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1 Chapter1. Solow growth Model 1. Introduction o Classical growth model : Baseline model o Importance of economic growth - 삶의질(standard of living) 을결정하는가장중요하고도기본적인요소 일반적으로일인당실질GDP 성장률로측정 o Rule of 70 - 실질소득이연간 % 로성장할경우실질소득이두배가되는데에는약 년이걸림 1960 년방글레데시와우리나라가 $1000의실질소득에서출발 우리나라와방글라데시의연평균성장률이 7% 와 2% 로가정 우리나라는 10 년(=70/7) 마다실질소득이 2 배로증가, 방글라데시는 35년 (70/2) 만다실질소득이 2 배로증가. 30년후인 1990년우리나라의실질소득 은 이되는반면방글라데시의실질소득수준은 $2,000 미만. o Questions - 경제성장율결정하는요인은무엇인가? - 왜어떤나라는높은경제성장률을기록하는반면다른나라는정해된성장률을 보이는가? 2. 기본가정들 o Inputs and output - Multiple inputs, single output o 생산함수 - 기업은주어진생산기술을하에서생산요소( 노동, 자본) 를결합하여산출물생산 - 생산함수(production function) 생산요소와산출물의관계를수학적으로표현 - : Labor augmenting technology, Effectiveness of labor - 1 -

2 노동의효율성을증가시키는생산기슬 동일한노동투입량에대한높은 ( 높은기술) 높은산출량수준 o - - 생산함수의확장 시간개념의도입 중요한가정 Constant return to scale 생산규모를 배증가 산출물 배증가 - 생산함수는영차동차함수 (homogeneous of degree 0) 모든투입량을, 배 배증가 : 효율적노동단위당자본투입량 (capital per effective labor) 효율적노동단위당자본산출량 (output per effective labor) EX) Cobb-Douglas 생산함수 : 영차동차 Marginal product of capital Marginal product of capital per effective labor,,, - 2 -

3 0 0 o 시간에따른변화 - Notation : Growth rate Ex) : 시간의변화에따른노동투입량의변화,,, labor growth rate,, technological progress o Capital stock 의변화 - National income identity : 저축률 :, - : 금용시장균형조건 - 3 -

4 - 자본스톡의변화 3. 동태모형 (Dynamics of Model) o 효율적노동단위량자본스톡의변화 - o Steady State( 정상상태) : Balanced growth, Long-run equilibrium - Steady state: - Steady state: 주요거시경제변수들이동일한비율로증가 : actual investment level = constant : break even investment level SS : : 효율적노동단위당자본스톡의수준이현상유지 자본스톡이닳아없어지는부분 : 효율적노동의성장부분 - 4 -

5 i actual investment < break even investment - 0 phase diagram o Balanced growth path : each variable grows at a constant rate - SS :, : exogenous variable?? =constant growth rate of = growth rate of - 5 -

6 - 1 인당? 로성장, 로성장 - Solow model growth rate of output per capita growth rate of capita stock per capita (growth rate of technology) 4. The impact of a change in the saving rate o SS condition in Solow growth model - - Most critical policy variable : are given o Permanent increase in saving - Impact an output - 6 -

7 - Output per worker constant grows at increase Grow at Level effect, but no growth effect - 7 -

8 Ex) Cobb-Douglas production S.S. o The impact on - Importance of welfare depends on consumption not on output depends on parameters If in S.S. by increase in by 증가된자본스톡으로부터얻어지는 부족 output이투자를높은수준에유지되는데 - 8 -

9 5. Quantitative Implication o Effect on output in long-run - - in S.S. : elasticity of output with respect ot, capital share of income increasing in - in most countries - 9 -

10 10% in output increase by 5% in the long run o Speed of convergence - How rapidly approachs to - - Frist order Taylor approximation at, at S.S., controls speed of convergence o Find - -, differential equation,,

11 o Numerical example - per year - : capital share - 매년 를 4% 줄여감 half로줄어드는데 년소요

12 6. Solow Model & Central Question of Growth theory o Solow model -, : grows at ( 기준진보) 시간에다른성장률차이설명 국가간성장률차이설명 o Difference in growth rate over time, and across countries - Factors affecting through production function Technological progress, - 자본의축적이 의성장률의차이를설명못함 - Solow Model: growth rate of, Only has permanent growth effect o Observation - 선진국의 은 100년전보다 10배증가 - 선진국은후진국보다 이 20~30배높음 - Cobb-Douglas production function Same across rich and poor counries Industrial countries is richer by 10 times than developing countries

13 : Couter factual 7. Empirical Application o Growth Accounting - 무엇이 의성장률을결정하는가? -, =Total factor productivity +, : Solow Residual : contribution of technological progress All sources other than capital accumulation Capital accumulation only explain 1/3 of output growth rate o Alwyn Young(1995) 1) - Asian countries have high growth rates investment high labor participation high Not technological progress o Convergence - Solow model: diminishing ( ) - Prediction 1) The Tyranny of Numbers: Confrontsny the stasticat Reality of East Asian growth Experience." Quarterly Journal of Economics 110,

14 Technology : diffusion over poor countries over time Poor countries catch up rich countries over time : Convergence o Empirical examinations for convergence 2) - If convergence(, perfect convergence) - Baumol(1986): 16개선진경제의 자료분석,, - Delong(1988) 의비판 sample selection problem: 성진경제만선택(long time periods 기준) measurement error ( 과거의 Data 는부정) Includes more countries and control measurement errors close to zero 2) Refer to the following studies Willam Baumal(1986). "productivity growth,convergence, and welfare," American Economic Revies Robert Barro and Xaver sala-i-matrin(1992). "convergence." Journal of Political Economy 100,

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