Macro chapter 3 and 2 summaries
Chapter 3 summaries
1. The basic Solow model studied in this chapter is characterized by the following features:
• Aggregate output, GOP, is produced from aggregate capital and aggregate labour
accordi'lg to a Cobb- Douglas production function with constant returns to capital and
labour and constant total factor productivity.
• Competitive market clearing ensures that the amounts of capital and labour used in
production in each period are equal to the predetemnined available amounts and that
factors are rewarded at their marginal products. An implication is that the income shares of
capital and labour are equal to the elasticities of output with respect to capital and labour,
respectively.
• Capital evolves over time such that from one year to the next, the change in the capital
stock equals gross saving (or investment) minus depreciation on the initial capital stock.
• In each period gross saving is an exogenous fraction of total income or GOP. Depreciation
on capital is given by an exogenous depreciation rate. The labour force changes over time
at an exogenous population growth rate.
2. The key assumptions of a Cobb- Douglas aggregate production function and a given rate of
saving and investment are motivated empirically by the relative constancy of income shares in
the long-run and the relative long-run constancy of the GOP share of total consumption
(private plus public), respectively.
3. The model implies that capital per worker and output per worker converge to particular
constant values in the long run. The convergence point defines the economy's steady state.
In steady state, consumption per worker, the real interest rate, and the wage rate are constant
as well. The steady state has some empirical plausibility with respect to the predicted value
for the long-run real interest rate and with respect to the long-run dependence of GOP per
worker on the investment rate and on the population growth rate.
4. The expressions for the steady state values of the key variables contain some sharp predictions
of how income per worker and consumption per worker depend on underlying parameters
in the long run. These predictions are of importance for the design of structural
policies to raise the standard of living. According to the model, policies to make a nation richer
should mainly be policies that can increase the investment share of GOP and bring population
growth under control, or policies to improve technology. To create a high level of consumption
per person, the savings and investment rate should not exceed the golden rule value,
which is equal to the elasticity of output with respect to capital.
5. In the model's steady state there is no positive growth in GOP per worker, consumption per
worker, or the real wage rate. This is at odds with the stylized facts of growth (in developed
economies). Remedying this shortcoming is one of the main purposes of the growth models
to be presented later. These models will contain some form of technological progress, such that total factor productivity increases over time. The basic Solow model does give rise to
(positive or negative) growth in output per worker during the transition to steady state. This
transitory growth is relatively long-lasting for plausible parameter values. Furthermore, the
process of transitory growth is such that the further below steady state an economy currently
is, the faster it will grow. This is in accordance with the observed conditional convergence
between the countries of the world.
6. Economics has much more to say about the sources of prosperity and growth than what can
be inferred from the basic Solow model. For instance, human capital (the education and
training embodied in people), and natural resources such as land, oil and metals are factors
of production which could be as important as physical capital and 'raw' labour. Furthermore,
the evolution of technology has to be an important determinant for long-run prosperity and
growth as well. These factors will be dealt with in later chapters, but the basic Solow model
is important as it stands. It is therefore worthwhile first modifying the model to take account of
a fact we have neglected in this chapter, namely the openness of real world economies. This
openness implies that capital can flow between countries at least to some extent. A Solow
model taking capital mobility appropriately into account and describing the accumulation of
capital and national wealth in an open economy will be presented in the next chapter.
Chapter 2 summaries
1. A country's GOP per worker may be used as a proxy for the average standard of living and the
average productivity of labour in the country. In some countries the population participates
much less in the formal market economy than in other countries. Focusing on GOP per
member of the offic ial labour force rather than on GOP per capita is a rough way of adjusting
for this.
2. The empirical evidence on levels of GOP per worker reveals enormous income d ifferences
across countries. Combining data on GOP per worker with data on population s ize, we found
that the relative cross-country income differences have declined a bit over the last 40 years,
but there was no reduction in international inequality at the bottom of the world income ladder.
The fact that the world income distribution has improved (slightly) in relative terms means that
on average poor countries have enjoyed percentage increases in income per worker at or
above the percentage increase in income per worker in the world in general. In absolute terms
poverty has therefore become less severe, but at the same time the absolute international
income differences between the richest and the poorest countries have increased.
3. The evidence shows that growth rates vary substantially across countries. By the process of
growing or declining quickly, a country can move from being re latively poor to being relatively
rich, or from being re latively rich to being relatively poor. Moreover, growth can break in a
country, turning from a high rate to a low one, or vice versa. These facts indicate that the fight
against poverty is not hopeless. On the other hand, a relatively prosperous country will not
automatically remain so regardless of the policies it follows . These observations point to the
importance of structural policies to promote or maintain economic growth.
4. The evidence seems to support the hypothesis that the world's countries converge in a conditional
sense: if one controls a ppropriately for structural differences across countries, a lower initial value of GOP per worker tends to be associated with a higher subsequent growth rate
in GOP per worker. In the long run income and GOP per worker thus converge to a countryspecific
growth path which is given by the country's basic structural characteristics {and
possibly also by its initial position).
5. Over periods of more than 130 years, and probably up to 200 years, many countries in
Western Europe and North America have had relatively constant annual rates of growth in
GOP per capita in the range 1.5- 2 per cent. During these long periods, labour's share of
GOP has stayed relatively constant. Hence the average real wage of a worker has grown by
approximately the same rate as GOP per worker. Furthermore, capital's share and the rate of
return on capital have shown no trend, so the capital- output ratio has been relatively constant,
that is, the stock of capital per worker has grown at roughly the same rate as GOP per
worker.
6. The facts just mentioned have given rise to an idealized picture of the process of constant
growth called 'balanced growth'.ln this book balanced growth will describe a situation where
GOP per worker, consumption per worker, the (average) real wage rate, and the
capital- labour ratio all grow at one and the same constant rate, and the rate of return on
capital is constant. We will use long-run accordance with balanced growth as an empirical
consistency check for the growth models to be presented in coming chapters.
1. The basic Solow model studied in this chapter is characterized by the following features:
• Aggregate output, GOP, is produced from aggregate capital and aggregate labour
accordi'lg to a Cobb- Douglas production function with constant returns to capital and
labour and constant total factor productivity.
• Competitive market clearing ensures that the amounts of capital and labour used in
production in each period are equal to the predetemnined available amounts and that
factors are rewarded at their marginal products. An implication is that the income shares of
capital and labour are equal to the elasticities of output with respect to capital and labour,
respectively.
• Capital evolves over time such that from one year to the next, the change in the capital
stock equals gross saving (or investment) minus depreciation on the initial capital stock.
• In each period gross saving is an exogenous fraction of total income or GOP. Depreciation
on capital is given by an exogenous depreciation rate. The labour force changes over time
at an exogenous population growth rate.
2. The key assumptions of a Cobb- Douglas aggregate production function and a given rate of
saving and investment are motivated empirically by the relative constancy of income shares in
the long-run and the relative long-run constancy of the GOP share of total consumption
(private plus public), respectively.
3. The model implies that capital per worker and output per worker converge to particular
constant values in the long run. The convergence point defines the economy's steady state.
In steady state, consumption per worker, the real interest rate, and the wage rate are constant
as well. The steady state has some empirical plausibility with respect to the predicted value
for the long-run real interest rate and with respect to the long-run dependence of GOP per
worker on the investment rate and on the population growth rate.
4. The expressions for the steady state values of the key variables contain some sharp predictions
of how income per worker and consumption per worker depend on underlying parameters
in the long run. These predictions are of importance for the design of structural
policies to raise the standard of living. According to the model, policies to make a nation richer
should mainly be policies that can increase the investment share of GOP and bring population
growth under control, or policies to improve technology. To create a high level of consumption
per person, the savings and investment rate should not exceed the golden rule value,
which is equal to the elasticity of output with respect to capital.
5. In the model's steady state there is no positive growth in GOP per worker, consumption per
worker, or the real wage rate. This is at odds with the stylized facts of growth (in developed
economies). Remedying this shortcoming is one of the main purposes of the growth models
to be presented later. These models will contain some form of technological progress, such that total factor productivity increases over time. The basic Solow model does give rise to
(positive or negative) growth in output per worker during the transition to steady state. This
transitory growth is relatively long-lasting for plausible parameter values. Furthermore, the
process of transitory growth is such that the further below steady state an economy currently
is, the faster it will grow. This is in accordance with the observed conditional convergence
between the countries of the world.
6. Economics has much more to say about the sources of prosperity and growth than what can
be inferred from the basic Solow model. For instance, human capital (the education and
training embodied in people), and natural resources such as land, oil and metals are factors
of production which could be as important as physical capital and 'raw' labour. Furthermore,
the evolution of technology has to be an important determinant for long-run prosperity and
growth as well. These factors will be dealt with in later chapters, but the basic Solow model
is important as it stands. It is therefore worthwhile first modifying the model to take account of
a fact we have neglected in this chapter, namely the openness of real world economies. This
openness implies that capital can flow between countries at least to some extent. A Solow
model taking capital mobility appropriately into account and describing the accumulation of
capital and national wealth in an open economy will be presented in the next chapter.
Chapter 2 summaries
1. A country's GOP per worker may be used as a proxy for the average standard of living and the
average productivity of labour in the country. In some countries the population participates
much less in the formal market economy than in other countries. Focusing on GOP per
member of the offic ial labour force rather than on GOP per capita is a rough way of adjusting
for this.
2. The empirical evidence on levels of GOP per worker reveals enormous income d ifferences
across countries. Combining data on GOP per worker with data on population s ize, we found
that the relative cross-country income differences have declined a bit over the last 40 years,
but there was no reduction in international inequality at the bottom of the world income ladder.
The fact that the world income distribution has improved (slightly) in relative terms means that
on average poor countries have enjoyed percentage increases in income per worker at or
above the percentage increase in income per worker in the world in general. In absolute terms
poverty has therefore become less severe, but at the same time the absolute international
income differences between the richest and the poorest countries have increased.
3. The evidence shows that growth rates vary substantially across countries. By the process of
growing or declining quickly, a country can move from being re latively poor to being relatively
rich, or from being re latively rich to being relatively poor. Moreover, growth can break in a
country, turning from a high rate to a low one, or vice versa. These facts indicate that the fight
against poverty is not hopeless. On the other hand, a relatively prosperous country will not
automatically remain so regardless of the policies it follows . These observations point to the
importance of structural policies to promote or maintain economic growth.
4. The evidence seems to support the hypothesis that the world's countries converge in a conditional
sense: if one controls a ppropriately for structural differences across countries, a lower initial value of GOP per worker tends to be associated with a higher subsequent growth rate
in GOP per worker. In the long run income and GOP per worker thus converge to a countryspecific
growth path which is given by the country's basic structural characteristics {and
possibly also by its initial position).
5. Over periods of more than 130 years, and probably up to 200 years, many countries in
Western Europe and North America have had relatively constant annual rates of growth in
GOP per capita in the range 1.5- 2 per cent. During these long periods, labour's share of
GOP has stayed relatively constant. Hence the average real wage of a worker has grown by
approximately the same rate as GOP per worker. Furthermore, capital's share and the rate of
return on capital have shown no trend, so the capital- output ratio has been relatively constant,
that is, the stock of capital per worker has grown at roughly the same rate as GOP per
worker.
6. The facts just mentioned have given rise to an idealized picture of the process of constant
growth called 'balanced growth'.ln this book balanced growth will describe a situation where
GOP per worker, consumption per worker, the (average) real wage rate, and the
capital- labour ratio all grow at one and the same constant rate, and the rate of return on
capital is constant. We will use long-run accordance with balanced growth as an empirical
consistency check for the growth models to be presented in coming chapters.
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