Cosmological growth of supermassive black holes: a synthesis model for accretion and feedback
The Solow growth model
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Transcript of The Solow growth model
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THE SOLOW GROWTH MODEL
skα
kα
k
δkStationary state
Production per worker
Gross investment per worker
Depreciation
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CONVERGENCE: GRAPHICAL APPROACH
-1-.5
0.5
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4 6 8 10 12lggdppc1980
GDP per cap real growth 1980-1990 Fitted values
Testing for convergence graphically:Put initial level on horizontal axis (here, income per capita)Put average growth rate over subsequent period on vertical axis
Convergence implies negative slope, divergence positive slope
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TESTING FOR CONVERGENCE IN A GROWTH EQUATION
-10
12
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4 6 8 10 12lggdppc2000
GDP per cap real growth 2000-2010 Fitted values
0 1 ,sample start 2 3-
i i i i ig Y I H u
0 1 ,sample starti i ig Y u -
Absolute convergence: typically, no… but
Conditional convergence: typically yes
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Growth-accounting equation
TOTAL FACTOR PRODUCTIVITY GROWTH & THE EAST ASIAN MIRACLE
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ln
ln
ln
ln
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it it it it
it it
it it
it it
it it
it it it it it
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Y t K L H
y Y
k K
L
h Hy k h u
e y k he e e TFPG
TFPG moy., 1970-90 (%
par an)Taiwan 3.76Hong-Kong 3.64Corée 3.10Japon 3.48Thailande 2.49Singapour 1.19Malaisie 1.07
Am. lat. 0.13Afr. sub-sah. -0.99
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Crude measure: (X + M)/GDP, biased by country size etcResidual measure (Leamer)
MEASURING OPENNESS
The Sachs-Warner (1995) measure of country openness
A country is «closed» if any of the following 5 criteria is met:
1. Average tariff above 40%2. Coverage ratio of non-tariff barriers (quotas, prohibitions etc.) above 40%3. Black-market premium on foreign exchange above 20% for a decade in a row4. Export monopoly (typically on a commodity export like cocoa, coffee)5. Socialist economy
0 1 2 3
predicted openness
residual
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i ii i i i
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i ii i
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X M POP LL REMOTENESS uGDP
X Mo eGDP
iX β
iX β
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Significantly higher growth performance for open economies
SACHS-WARNER CLASSIC RESULT
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But… Rodriguez/Rodrik critique suggests it’s not trade policy that did the trick
RODRIGUEZ-RODRIK CRITIQUE
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HOW CROSS-SECTIONAL DATA CAN OBFUSCATE CAUSAL LINKS
Year Opening Growth Opening Growth1 0 0.3 1 1.52 1 5.1 1 2.1Average 0.5 2.7 1 1.8
Country 1 Country 2
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Time averages “Panel”
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Wacziarg-Welsh use factual information about trade-policy changes
WACZIARG-WELSH 2008: USING PANEL DATA
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PANEL RESULTS ARE ROBUST
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WACZIARG WELSH: GROWTH BEFORE & AFTER LIBERLIZATION
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EXPLAINING THE GROWTH ACCELERATION: INVESTMENT