14.451 Lecture Notes Economic Growth

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George-Marios Angeletos • In the Cobb-Douglas case, y = k α , the convergence rate is simply −λ =(1− α)(δ + n), where α is the income share of capital. Note that as λ → 0 as α → 1. That is, convergence becomes slower and slower as the income share of capital becomes closer and closer to 1. Indeed, if it were α =1, the economy would a balanced growth path. • In the example with productive government spending, y = k α g β = k α/(1−β) τ β/(1−β) , we get µ −λ = 1 − α (δ + n) 1 − β The convergence rate thus decreases with β, the productivity of government services. And λ → 0 as β → 1 − α. • Calibration: If α = 35%, n=3%(=1%population growth+2% exogenous technolog- ical process), and δ =5%, then −λ =6%. This contradicts the data. But if α = 70%, then −λ =2.4%, which matches the date. 2.5 Cross-Country Differences and Conditional Con- vergence. 2.5.1 Mankiw-Romer-Weil: Cross-Country Differences • The Solow model implies that steady-state capital, productivity, and income are deter- mined primarily by technology (f and δ), the national saving rate (s), and population growth (n). 34
14.451 Lecture Notes • Suppose that countries share the same technology in the long run, but differ in terms of saving behavior and fertility rates. If the Solow model is correct, observed cross- country income and productivity differences should be explained by observed cross- country differences in s and n, • Mankiw, Romer and Weil tests this hypothesis against the data. In it’s simple form, the Solow model fails to explain the large cross-country dispersion of income and productivity levels. • Mankiw, Romer and Weil then consider an extension of the Solow model, that includes two types of capital, physical capital (k) and human capital (h). Output is given by y = k α h β , where α>0,β > 0, and α + β
Page 1 and 2: 14.451 Lecture Notes Economic Growt
Page 3 and 4: Contents Preface ix 1 Introduction
Page 5 and 6: 14.451 Lecture Notes 3.1.4 OptimalC
Page 7 and 8: 14.451 Lecture Notes 5.2 SomeExampl
Page 9 and 10: Preface This is the set of lecture
Page 11 and 12: Chapter 1 IntroductionandGrowthFact
Page 13 and 14: 14.451 Lecture Notes 1.2 The World
Page 15 and 16: 14.451 Lecture Notes • Figure 4 3
Page 17 and 18: 14.451 Lecture Notes 9. Openness: I
Page 19 and 20: Chapter 2 The Solow Growth Model (a
Page 21 and 22: 14.451 Lecture Notes • We say tha
Page 23 and 24: 14.451 Lecture Notes 2.1.3 The Reso
Page 25 and 26: whereas consumption is given by 14.
Page 27 and 28: 14.451 Lecture Notes where the latt
Page 29 and 30: 14.451 Lecture Notes 2.2 Decentrali
Page 31 and 32: 14.451 Lecture Notes • Let K m t
Page 33 and 34: Equivalently, 14.451 Lecture Notes
Page 35 and 36: 14.451 Lecture Notes where Kt ≡ R
Page 37 and 38: 14.451 Lecture Notes Proof. Follows
Page 39 and 40: 14.451 Lecture Notes • Combining
Page 41 and 42: 14.451 Lecture Notes We would expec
Page 43: • Straightforward algebra gives W
Page 47 and 48: 2.6 Miscellaneous 14.451 Lecture No
Page 49 and 50: 14.451 Lecture Notes 2.6.3 Introduc
Page 51 and 52: Chapter 3 The Neoclassical Growth M
Page 53 and 54: 14.451 Lecture Notes ut+1 : There i
Page 55 and 56: 14.451 Lecture Notes • Combining
Page 57 and 58: Equivalently, taking (kt,kt+2) as g
Page 59 and 60: equivalently 14.451 Lecture Notes
Page 61 and 62: 14.451 Lecture Notes • Let B be t
Page 63 and 64: 14.451 Lecture Notes 3.2 Decentrali
Page 65 and 66: 14.451 Lecture Notes only the total
Page 67 and 68: 14.451 Lecture Notes • Finally, i
Page 69 and 70: 14.451 Lecture Notes The constraint
Page 71 and 72: 14.451 Lecture Notes where f(k) ≡
Page 73 and 74: 14.451 Lecture Notes Proposition 15
Page 75 and 76: 14.451 Lecture Notes individual’s
Page 77 and 78: 14.451 Lecture Notes 3.3 Steady Sta
Page 79 and 80: 3.3.2 Transitional Dynamics 14.451
Page 81 and 82: 14.451 Lecture Notes Proof. The pol
Page 83 and 84: 14.451 Lecture Notes • The ˙c =0
Page 85 and 86: 14.451 Lecture Notes 3.5 Comparativ
Page 87 and 88: 14.451 Lecture Notes • We conclud
Page 89 and 90: where At denotes TFP. Note that 14.
Page 91 and 92: 14.451 Lecture Notes • Note that
Page 93 and 94: 14.451 Lecture Notes 3.6.2 Impulse
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Chapter 4 Applications 4.1 Arrow-De
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14.451 Lecture Notes bles. We can t
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14.451 Lecture Notes • Then, the
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14.451 Lecture Notes • More gener
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14.451 Lecture Notes • Consider n
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14.451 Lecture Notes aggregate path
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14.451 Lecture Notes notes to be co
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Chapter 5 Overlapping Generations M
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14.451 Lecture Notes Life-cycle con
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Note that Recall that ∂m ∂R 14.
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where the scalar ζ>0 is given by 1
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14.451 Lecture Notes • Finally, n
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Chapter 6 Endogenous Growth I: AK,
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14.451 Lecture Notes so that consum
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14.451 Lecture Notes • Finally, t
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14.451 Lecture Notes • Combining
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14.451 Lecture Notes Like in the si
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14.451 Lecture Notes Combining the
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14.451 Lecture Notes • Households
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14.451 Lecture Notes Proposition 25
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Chapter 7 Endogenous Growth II: R&D
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14.451 Lecture Notes More generally
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14.451 Lecture Notes you can think
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14.451 Lecture Notes Free entry in
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14.451 Lecture Notes 7.1.8 Pareto A
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14.451 Lecture Notes 7.1.9 Introduc
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7.2.2 The Value of Innovation 14.45
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14.451 Lecture Notes It follows tha
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14.451 Lecture Notes • Compare no
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