The Facts of Growth Growth is the steady increase in aggregate output over time. We now shift our focus from economic fluctuations and the determination.

The Facts of Growth Growth is the steady increase in aggregate output over time. We now shift our focus from economic fluctuations and the determination of output in the short and medium run to growth and the determination of output in the long run.

Figure 10-1 U.S. GDP since 1890. U.S. GDP per person since 1890
Panel A Panel A shows the enormous increase in U.S. output since 1890, by a factor of 46.

Figure 10-1 U.S. GDP since 1890. U.S. GDP per person since 1890 (cont’d)
Panel B Panel B shows that the increase in output is not simply the result of the large increase in U.S. population from 63 million to more than 300 million over this period. Output per person has risen by a factor of 9.

10-1 Measuring the Standard of Living
We care about growth because we care about the standard of living. Output per person, rather than output itself, is the variable we compare over time or across countries. We need to correct for variations in exchange rates and systematic differences in prices across countries. When comparing the standard of living across countries, we use purchasing power parity (PPP) numbers which adjust the numbers for the purchasing power of different countries. The right measure on the production side is output per worker or output per hour worked.

FOCUS: The Construction of PPP Numbers
Consider this example: United States: Each year, people buy a new car for $10,000, and spend another $10,000 on food. Russia: People spend 20,000 rubles on cars (each lasts for 15 years) a year, and 40,000 rubles on food. If the exchange rate is $1 = 30 rubles, consumption per person in Russia is only 10% of U.S. consumption per person. If we use U.S. prices for both countries and assume people spending all money on food, then consumption per person is $20,000 ($10,000+$10,000) in the U.S., but $10,700 [(1/15)x$10,000)=(1x$10,000)] in Russia, so Russian consumption per person is 53.5% of U.S. consumption per person.

10-2 Growth in Rich Countries since 1950
Table The Evolution of Output per Person in Four Rich Countries since 1950 There has been a large increase in output per person due in part to the force of compounding. There has been a convergence of output per person across countries.

FOCUS: Does Money Lead to Happiness?
Figure 1 Life Satisfaction and Income per Person Easterlin paradox: Once basic needs are satisfied, higher income per person does not increase happiness, and the level of income relative to others, rather than the absolute level of income, matters

10-2 Growth in Rich Countries since 1950
Figure Growth Rate of GDP Per Person since 1950 versus GDP per Person in 1950; OECD Countries Countries with lower levels of output per person in 1950 have typically grown faster.

10-3 A Broader Look across Time and Space
From the end of the Roman Empire to roughly year 1500, Europe was in a Malthusian trap or Malthusian era with stagnation of output per person because most workers were in agriculture with little technological progress. After 1500, growth of output per person turned positive but still small. Between 1820 and 1950, U.S. growth was still 1.5% per year. Sustained growth was high since 1950.

Figure Growth Rate of GDP per Person since 1960, versus GDP Per Person in 1960 (2005 dollars); 85 Countries There is no clear relation between the growth rate of output since 1960 and the level of output per person in 1960.

For the OECD countries, there is clear evidence of convergence. Convergence is also visible for many Asian countries, especially for those with high growth rates, called the four tigers—Singapore, Taiwan, Hong Kong, and South Korea. Most African countries were very poor in 1960, and some of them had negative growth of output per person between 1960 and 2011 due in part to internal or external conflicts.

10-4 Thinking About Growth: A Primer
Aggregate production function F: where Y is output, K is capital, and N is labor. The function F depends on the state of technology. Constant returns to scale: Decreasing returns to capital: Increases in capital lead to smaller and smaller increases in output. Decreasing returns to labor: Increases in labor lead to smaller and smaller increases in output.

The production function and constant returns to scale imply a simple relation between output per worker (Y/N) and capital per worker (K/N): Increases in capital per worker: Movements along the production function. Improvements in the state of technology: Shifts (up) of the production function. Growth comes from capital accumulation (a higher saving rate) and technological progress (the improvement in the state of technology).

Figure Output and Capital per Worker Decreasing returns to capital: Increases in capital per worker lead to smaller and smaller increases in output per worker.

Figure The Effects of an Improvement in the State of Technology An improvement in technology shifts the production function up, leading to an increase in output per worker for a given level of capital per worker.

Saving, Capital Accumulation, and Output
Since 1970, the U.S. saving ratio—the ratio of saving to gross domestic product—has averaged only 17%, compared to 22% in Germany and 30% in Japan. Even if a lower saving rate does not permanently affect the growth rate, it does affect the level of output and the standard of living.

11-1 Interactions between Output and Capital
Output in the long run depends on two relations: The amount of capital determines the amount of output The amount of output being produced determines the amount of saving, which in turn determines the amount of capital being accumulated over time

Figure Capital, Output, and Saving/Investment

Recall Chapter 10: or Assume that N is constant, and there is no technological progress, so f does not change over time: Higher capital per worker leads to higher output per worker.

Assume: The economy is closed: I = S + (T − G) Public saving (T − G) is 0: I = S Private saving is proportional to income: S = sY So the relation between output and investment: It = sYt Investment is proportional to output. The higher (lower) output is, the higher (lower) is saving and so the higher (lower) is investment.

The evolution of the capital stock is: Replace investment by the above expression and divide both sides by N: or The change in the capital stock per worker is equal to saving per worker minus depreciation.

11-2 The Implications of Alternative Saving Rates
Combining equations (11.1) and (11.2): If investment per worker exceeds (is less than) depreciation per worker, the change in capital per worker is positive (negative).

Figure Capital and Output Dynamics When capital and output are low, investment exceeds depreciation and capital increases. When capital and output are high, investment is less than depreciation and capital decreases.

The state in which output per worker and capital per worker are no longer changing is called the steady state of the economy. The steady-state value of capital per worker is such that the amount of saving per worker is sufficient to cover depreciation of the capital stock per worker.

Focus: Capital Accumulation and Growth in France in the Aftermath of World War II
France suffered heavy losses in capital when World War II ended in 1945. The growth model predicts that France would experience high capital accumulation and output growth for some time. From 1946 to 1950, French real GDP indeed grew at 9.6% per year. Table 1 Proportion of the French Capital Stock Destroyed by the End of World War II

The saving rate has no effect on the long-run growth rate of output per worker, which is equal to zero. The saving rate determines the level of output per worker in the long run. An increase in the saving rate will lead to higher growth of output per worker for some time, but not forever.

Figure The Effects of Different Saving Rates A country with a higher saving rate achieves a higher steady-state level of output per worker.

What matters to people is not how many is produced, but how much they consume. Governments can affect the saving rate by: changing public saving (budget surplus) using taxes to affect private saving Golden-rule level of capital: The level of capital associated with the saving rate that yields the highest level of consumption in steady state.

Figure The Effects of the Saving Rate on Steady-State Consumption per Worker An increase in the saving rate leads to an increase, then to a decrease in steady-state consumption per worker.

For a saving rate between zero and the golden-rule level, a higher saving rate leads to higher capital per worker, higher output per worker and higher consumption per worker. For a saving rate greater than the golden-rule level, a higher saving rate still leads to higher capital per worker and output per worker, but lower consumption per worker. An increase in the saving rate leads to lower consumption for some time but higher consumption later.

11-3 Getting a Sense of Magnitudes
Assume the production function f: so that equation (11.3) becomes: which describes the evolution of capital over time.

FOCUS: Social Security, Saving, and Capital Accumulation in the United States
Social Security, introduced in 1935, has led to a lower U.S. saving rate and thus lower capital accumulation and lower output per person in the long run. Social Security is a pay-as-you-can system that taxes workers and redistributes the tax contributions as benefits to current retirees, resulting in lower private saving as workers anticipate receiving benefits when they retire. An alternative is a fully-funded system that pays back the principal plus interest to the workers when they retire, resulting in lower private saving but higher public saving as the System invests their contributions in financial assets.

Equation (11.7) implies that capital per worker in the steady state (K*/N) becomes: Combining equations (11.6) and (11.8) gives the steady state output per worker: In the long run, output per worker doubles when the saving rate doubles.

Figure 11-7(a) The Dynamic Effects of an Increase in the Saving Rate from 10% to 20% on the Level and the Growth Rate of Output per Worker It takes a long time for output to adjust to its new higher level after an increase in the saving rate. Put another way, an increase in the saving rate leads to a long period of higher growth.

Figure 11-7(b) The Dynamic Effects of an Increase in the Saving Rate from 10% to 20% on the Level and the Growth Rate of Output per Worker It takes a long time for output to adjust to its new higher level after an increase in the saving rate. Put another way, an increase in the saving rate leads to a long period of higher growth.

In the steady state, consumption per worker is: Given equations (11.8) and (11.9), the steady-state consumption per worker is: Table 11-1 gives the steady-state values of capital per worker, output per worker and consumption per worker for different saving rates (given δ=10%)

Table The Saving Rate and the Steady-State Levels of Capital, Output, and Consumption per Worker

11-4 Physical versus Human Capital
Human capital (H): The set of skills of the workers in the economy built through education and on-the-job training. The production function with human capital: As for physical capital (K) accumulation, countries that save more or spend more on education can achieve higher steady-state levels of output per worker.

11-4 Physical versus Human Capital
Models of endogenous growth: Steady-state growth in outpour per worker depends on variables such as the saving rate and the rate of spending on education, even without technological progress. However, the current consensus is that given the rate of technological progress, higher rates of saving or spending on education do not lead to a permanently higher growth rate.

APPENDIX: The Cobb-Douglas Production Function and the Steady State
which gives a good description of the relation between output, physical capital, and labor in the United States from 1899 to 1922. In steady state, saving per worker must be equal to depreciation per worker, implying that: s(K*/N)α = δ(K*/N) where K* is the steady-state level of capital.

APPENDIX: The Cobb-Douglas Production Function and the Steady State
The preceding expression can be rewritten as: s = δ(K*/N) 1-α The steady-state level of capital per worker becomes: (K*/N) = (s/δ) α/(1-α) If α = 0.5, then: K*/N = s/δ which implies that a doubling of the saving rate leads to a doubling in steady-state output per worker.

12-1 Technological Progress and the Rate of Growth
Technological progress can lead to: larger quantities of output for given quantities of capital and labor better products new products a large variety of products The state of technology (A) is a variable that tells us how much output can be produced from given amounts of capital and labor at any time: so AN is the amount of effective labor.

With constant returns to scale and a given state of technology (A), if the amounts of capital and labor changes by x times, output changes by x times: If x = 1/AN, output per effective worker is a function of capital per effective worker:

Figure Output per Effective Worker versus Capital per Effective Worker Because of decreasing returns to capital, increases in capital per effective worker lead to smaller and smaller increases in output per effective workers.

Recall Chapter 11: I = S = sY, so that equation (12.2) becomes (lower curve in Figure 12-2): The line in Figure 12-2 shows the level of investment per effective worker needed to maintain a given level of capital per effective worker because: where δ is the capital depreciation rate, gA is the rate of technological progress, and gN is the rate of population growth.

Figure The Dynamics of Capital per Effective Worker and Output per Effective Worker Capital per effective worker and output per effective worker converge to constant values in the long run.

The steady state of the economy is such that capital per effective worker and output per worker are constant, and equal to (K/AN)* and (Y/AN)*, respectively. When the economy is in steady state, output per worker grows at the rate of technological progress (gA).

Table The Characteristics of Balanced Growth

On the balanced growth path (steady state or long run): Capital per effective worker and output per worker are constant. Capital per worker and output per worker are growing at the rate of technological progress. Capital and output are growing at a rate equal to the sum of population growth and the rate of technological progress.

Figure The Effects of an Increase in the Saving Rate: I An increase in the saving rate leads to an increase in the state-state levels of output per effective worker and capital per effective worker.

12-2 The Determinants of Technological Progress
Most technological progress is the outcome of firms’ research and development (R&D) activities. The level of R&D spending depends not only on the fertility of research (how spending on R&D translates into new ideas and new products) but also on the appropriability of research results (the extent to which firms can benefit from the results of their own R&D). Patents give a firm that has discovered a new product the right to exclude anyone else from the production or use of that new product for some time.

FOCUS: The Diffusion of New Technology: Hybrid Corn
Figure 1 Percentage of Total Corn Acreage Planted with Hybrid Seed, Selected U.S. States, 1932–1956 Each state’s speed of adopting hybrid corn, which increased the corn yield by up to 20%, was a function of its profitability.

FOCUS: Management Practices: Another Dimension of Technological Progress
Some researchers believe that management practices might be stronger than many of the other factors that determine a firm’s performance, including technological innovations. In a study of management practices and performance of more than 4,000 medium-sized manufacturing operations in Europe, the U.S. and Asia, two economists found that firms used the same technology but applied good management practices perform significantly better than those that did not.

12-2 The Determinants of Technological Progress
To sustain growth, advanced countries that are at the technology frontier must innovate. The difference between innovation and imitation explains why countries that are less technologically advanced often have poor patent protection.

12-3 Institutions, Technological Progress, and Growth
Figure Protection from Expropriation and GDP per Person There is a strong positive relation between the degree of protection from expropriation and the level of GDP per person. This highlights the importance of the protection of property rights.

FOCUS: The Importance of Institutions: North Korea and South Korea
Figure 1 PPP GDP per Person: North and South Korea, 1950−1998 After the Korean War, South Korea has provided private ownership and legal protection of private producers, while North Korea relied on central planning with no property rights for individuals. Fifty years later, GDP per person was 10 times higher in South Korea.

FOCUS: What Is Behind Chinese Growth?
Average growth of output per worker in China has increased from 2.5% between 1977, to more than 9% since then. Unlike Central and Eastern Europe, China’s state sector has declined slowly and that decline has been more than compensated by strong private sector growth. Also, the Chinese political system did not change, and the government was able to control the pace of transition to a market economy. As property rights are still not well established and the banking system is still inefficient, the limits of Chinese growth are clear.

12-4 The Facts of Growth Revisited
Table Average Annual Rates of Growth of Output per Worker and Technological Progress in Four Rich Countries since 1985 Over the period 1985–2014, output per worker has grown at rather similar rates across the five countries. Growth since 1985 has mostly come from technological progress, not from unusually high capital accumulation.

12-4 The Facts of Growth Revisited
Table Average Annual Rate of Growth of Output per Worker and Technological Progress in China, 1978–2011 Over the period 1978–1995, China was on a balanced growth path as the rate of technological progress was close to the rate of growth of output per worker. Since 1996, although growth of output per worker has remained high, the contribution of technological progress has decreased. Technological progress in China comes from productivity growth due to labor transferring from the countryside to cities, and imported technology from more technologically advanced countries.

13-1 Productivity, Output, and Unemployment in the Short Run
For simplicity, we ignore capital so that the production function becomes: so output is produced using only labor. Rewrite equation (13.1) as: so employment equals output divided productivity. In the short run, output is determined by the IS and LM relations:

Figure The Demand for Goods in the Short Run following an increase in Productivity An increase in productivity may increase or decrease the demand for goods. Thus, it may shift the IS to the left or to the right. What happens depends on what triggered the increase in productivity in the first place.

Figure Labor Productivity and Output Growth in the United States since 1960 There is a strong positive relation between output growth and productivity growth. But the causality runs from output growth to productivity, not the other way around.

In the medium run, the economy tends to return to the natural level of unemployment. Is the natural rate of unemployment itself affected by changes in technology? The theme of technological unemployment typically resurfaces whenever unemployment is high, e.g., the Great Depression. Because the natural rate of unemployment is determined by the price-setting relation and the wage-setting relation (Chapter 7), we can consider how changes in technology affect each of the two relations.

Assumptions for Price setting: Equation (13.1) implies that each worker produces A units of output. The nominal cost of producing 1 unit of output is (1/A)W = W/A, where W is the nominal wage. Firms set price with the markup m, so that Assumption for wage setting: which is an extension of equation (7.1), so that wages reflect the increase in productivity.

Assumption for wage setting: where “e” represented the expected level. Equation (13.4) is an extension of equation (7.1), so that wages reflect the increase in productivity. Reorganizing equation (13.3): If Pe=P and Ae=A, then equation (13.4) becomes:

13-2 Productivity and the Natural Rate of Unemployment
Figure The Effects of an Increase in Productivity on the Natural Rate of Unemployment An increase in productivity shifts both the wage and the price-setting curves by the same proportion and thus has no effect on the natural rate.

Figure Productivity Growth and Unemployment. Averages by Decade, 1890−2014 This is little relation between the 10-year averages of productivity growth and the 10-year averages of the unemployment rate. If anything, higher productivity growth is associated with lower unemployment.

Figure The Effects of a Decrease in Productivity Growth on the Unemployment Rate When Expectations of Productivity Growth Adjust Slowly If it takes time for workers to adjust their expectations of productivity growth, a slowdown in productivity growth will lead to an increase in the natural rate for some time.

In the short run, there is no reason to expect a systematic relation between movements in productivity growth and movements in unemployment. In the medium run, if there is a relation between productivity growth and unemployment, it appears to be an inverse relation. Fears of technological unemployment probably come from structural change—the change in the structure of the economy induced by technological progress.

13-3 Technological Progress, Churning, and Inequality
Harvard economist Joseph Schumpeter emphasized in the 1930s that the process of growth is a process of creative destruction—new goods make old ones obsolete. Churning: New techniques of production require new skills, making some old skills less useful. Evidence of wage inequality: Workers with low (high) levels of education have seen their relative wage fall (rise) steadily over time.

FOCUS: Job Destruction, Churning, and Earnings Losses
Two economists found that mass layoffs cause enormous relative earnings declines whether they occur in a recession or an expansion. Figure 1 Earnings Losses of Workers Who Experience a Mass Layoff

FOCUS: The Long View: Technology, Education, and Inequality
Returns to education measured by wage differentials have provided economic incentives for people to stay in school longer. Two economists found that technological progress that is accompanied by an increase in the demand for skilled and educated workers, does not necessarily increase economic inequality. Figure 1 Wage Differentials and the Returns to Education, 1939 to 1995

Figure Evolution of Relative Wages by Education Level, 1973−2012 Since the early 1980s, the relative wages of workers with a low education level have fallen; the relative wages of workers with a high education level have risen.

Wage inequality is largely caused by a steady increase in the demand for high-skilled workers relative to the demand for low-skill workers because: International trade: U.S. firms that employ higher proportions of low-skill workers are increasingly driven out of markets by imports from similar firms in low-wage countries. Skilled-biased technological progress: New machines and new methods of production require more and more high skill workers.

Figure The Evolution of the Top 1% Income Share in the United States since 1913 Top 1% refers to the top percentile. In 2014, these were families with annual income (including capital gains) above $387,000. Top 1% to 5% is the next 4%, with annual income between $167,000 and $387,000. Top 5% to 10% is the bottom half of the top decile; families with annual income between $118,000 and $167,000. Income is defined as annual gross income reported on tax returns excluding all government transfers.

Figure The Top Income Share and Patenting in the United States, 1963−2013 The figure plots the number of patent applications per 1,000 inhabitants against the top 1% income share. Observations span the years between 1963 and 2013.

The Facts of Growth Growth is the steady increase in aggregate output over time. We now shift our focus from economic fluctuations and the determination.

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The Facts of Growth Growth is the steady increase in aggregate output over time. We now shift our focus from economic fluctuations and the determination.

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