ECON 214: Intermediate MacroeconomicsChapter 2 - Macroeconomic Dynamics

2.1 - Economic Growth

Andreas Pollak

Department of EconomicsUniversity of Saskatchewan

Winter 2020/21

Overview

Chapter 2.1 - Economic Growth

The Solow Model

capital accumulationsteady state and dynamicsproductivity and population growthdynamic efficiency

Growth Accounting

Readings

Williamson, Chapter 7

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GDP and Standard of Living

Countries by GDP (PPP) per capita in 2020

Data source: IMF.Image: Wikipedia.

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GDP and Standard of Living

GDP per capita (in 2019 USD) and average growth rates

Country 1960 2019 growth (% p.a.)

Luxembourg 15,127.9 114,704.6 3.5Switzerland 12,060.5 81,993.7 3.3United States 20,290.4 65,297.5 2.0Finland 7,958.0 48,782.8 3.1Germany 46,445.2Canada 15,482.8 46,194.7 1.9WORLD 3,039.1 11,441.7 2.3Russian Federation 11,585.0China 603.9 10,261.7 4.9Mexico 2,307.6 9,946.0 2.5Botswana 391.4 7,961.3 5.2India 548.6 2,099.6 2.3Kenya 658.6 1,816.5 1.7Burundi 474.3 261.2 -1.0

Data sources: World Bank (current GDP), FRED (GDP deflator).

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GDP and Standard of Living

Original Income avg. growth rate income after 30 years increase

$1 0% $1.00 0%$1 1% $1.35 35%$1 2.5% $2.10 110%$1 5% $4.32 332%$1 8% $10.06 906%

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GDP and Standard of Living

Source: Barro/Sala-i-Martin (2003): Economic Growth.

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GDP and Standard of Living

Source: Barro/Sala-i-Martin (2003): Economic Growth.

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GDP and Standard of Living

Source: Barro/Sala-i-Martin (2003): Economic Growth.

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GDP and Standard of Living

Per-capita GDP in selected countries, 1-2003 ADmeasured in 1990 international dollars

1 1000 1500 1600 1700 1820 1870 1913 1950 1973 2003

France 473 425 727 841 910 1,135 1,876 3,485 5,271 13,114 21,861Italy 809 450 1,100 1,100 1,100 1,117 1,499 2,564 3,502 10,634 19,151NL 425 425 761 1,381 2,130 1,838 2,757 4,049 5,996 13,082 21,480UK 400 400 714 974 1,250 1,706 3,190 4,921 6,939 12,025 21,310US 400 400 400 400 527 1,257 2,445 5,301 9,561 16,689 29,037China 450 450 600 600 600 600 530 552 448 838 4,803Japan 400 425 500 520 570 669 737 1,387 1,921 11,434 21,218

Data source: Maddison (2007).

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GDP and Standard of Living

Source: Williamson.

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ECON 214: Intermediate MacroeconomicsChapter 2 - Macroeconomic Dynamics

2.1 - Economic Growth

Chapter 2.1.1 - The Solow Model - A Simple Version

The Solow Model

Definition: Steady-State Equilibrium

A steady-state equilibrium is an equilibrium in which the economy doesnot change over time.

In our model: k is constant, i.e. k ′ = k

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The Solow Model

Source: Williamson.

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The Solow Model

Source: FRED (Federal Reserve Bank of St. Louis).

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The Solow Model

Source: FRED (Federal Reserve Bank of St. Louis).

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ECON 214: Intermediate MacroeconomicsChapter 2 - Macroeconomic Dynamics

2.1 - Economic Growth

Chapter 2.1.2 - The Solow Model with Population Growthand Technological Progress

The Solow Model

Approximate Growth Rate Arithmetics

We will use a hat to label the growth rate of a variable x : x = x ′−xx

For small growth rates or percentage changes, we can use the followingapproximations:For a product xy : xy ≈ x + y

For a quotient x/y : x/y ≈ x − yFor a power function xα: xα ≈ αx

Population N grows at the constant rate N = n.The productivity E of workers grows at the constant rate E = g .

Y = F (K , EN︸︷︷︸“effective labour”

)

E : labour-augmenting technologyg : rate of labour-augmenting technological progress

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The Solow Model

Observations:

In a steady state,

“per-effective labour” variables (y , k , i , c) are constant,

per capita variables (y , k, i , c) grow at the rate g , and

aggregate variables (Y , K , I , C ) grow at the rate n + g .

All steady-state growth rates are determined by n and g !

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The Solow Model

Source: Williamson.

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The Solow Model

Level vs. growth effects:

Everything else equal, in a steady state,

higher investment i = sy leads to a higher level of per capita variables(y , k , and – if dynamically efficient – c),

higher population growth n leads to a lower level of per capitavariables (y , k , c),

faster technological progress g leads to a lower level but highergrowth rate of per capita variables (y , k, c).

A higher rate of productivity growth g is the only thing that leads to ahigher growth rate of per capita variables in the long run.

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The Solow Model

Numerical Example: Economic Growth

Given:production technology: F (K ,N) = 33K

13N

23

population growth n = 1%, rate of technological progress g = 2%,depreciation rate d = 8%, saving rate s = 3

16Follow these steps:

write down the capital accumulation equation in per-effective-labourunits

find the steady-state capital stock k∗

solve for the other steady state variables of interest (y∗, c∗)

find the Golden-Rule saving rate s∗∗ and the correspondingsteady-state values k∗∗, y∗∗, c∗∗

using a spreadsheet, find the half life of the capital gap whentransitioning to the Golden-Rule steady state starting at k0 = 500

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ECON 214: Intermediate MacroeconomicsChapter 2 - Macroeconomic Dynamics

2.1 - Economic Growth

Chapter 2.1.3 - Growth Accounting

Growth Accounting

A Growth Accounting Example

component value weight total contribution

output Y 3% 1 3%

capital K 3% α = 13

1%

labour N 1.5% 1− α = 23

1%

TFP z Y − αK − (1− α)N = 1% 1 1%...or, if you are interested in labour productivity rather than TFP:

labour productivity E 11−α

z = 32z = 1.5% 1− α = 2

31%

Overall, we have:Y = z + αK − (1 − α)NorY = αK − (1 − α)(E + N)

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Growth Accounting

Source: Williamson.

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Growth Accounting

Source: Williamson, 4th Canadian Edition.

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ECON 214: Intermediate MacroeconomicsChapter 2 - Macroeconomic Dynamics

2.1 - Economic Growth

Chapter 2.1.4 - Growth: The Bigger Picture

Theories of Economic Growth

pre-industrial (Malthusian) vs. recent growth experience

1200 1300 1400 1500 1600 1700 1800 1900 2000 210010 -1

100

101

102

103

102

103

104

105Great Britain: Historical Data

population (index)GDP (real, index)per-capita GDP (2014 pounds, right axis)

Data source: Bank of England: A Millennium of Macroeconomic Data.https://www.bankofengland.co.uk/statistics/research-datasets

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Growth vs Business Cycles

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Growth, Convergence and Poverty

Per-capita GDP relative to US (constant 2010 USD)

1960 1965 1970 1975

40

50

60

70

80

90

100

110

120

per-

capi

ta G

DP

[% o

f US

]

GDP in Canada

CanadaAustraliaFranceItalySpainGreeceJapan

Data Source: World Bank via FRED.

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Growth, Convergence and Poverty

Per-capita GDP relative to US (constant 2010 USD)

1960 1970 1980 1990 2000 2010

100

101

102

per-

capi

ta G

DP

[% o

f US

]

GDP in Canada

CanadaAustraliaFranceItalySpainGreeceJapanKoreaChinaIndiaArgentinaMozambique

Data Source: World Bank via FRED.

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Growth, Convergence and Poverty

Source: Williamson.

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Growth, Convergence and Poverty

Source: Barro (2008): Macroeconomics – A Modern Approach.

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