## wpiea2019208-print-pdf

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---

### Okun’s law — definition and key equations
- Okun’s law (level form):
  - u_t − u*_t = −β (Y_t − Y*_t)  (equation (1))
  - where u_t is unemployment, u*_t the NAIRU, Y_t the log of GDP, and Y*_t the log of potential GDP.
- First-difference form (assuming ∆u*_t = 0):
  - ∆u_t = β ∆Y*_t − β ∆Y_t  (equation (2))
- 10-year rolling regression specification used to track Okun dynamics:
  - ∆u_t = α − β ∆Y_t  (equation (3))

### Interpretation: movements along vs. shifts of the Okun curve
- If GDP growth (∆Y_t) slows while potential output growth (∆Y*_t) remains unchanged:
  - This generates a leftward movement along the existing Okun curve.
- If potential output growth (∆Y*_t) falls:
  - The Okun curve shifts to the left.
- Empirical implication highlighted:
  - The observed slowdown in GDP growth accompanied by falling unemployment is consistent with a leftward shift of the Okun curve driven by a slowdown in potential output growth, not solely weak aggregate demand.

### Empirical evidence and regression results
- Visual and regression evidence:
  - Figure 2.1: shows the Okun curve has shifted left, consistent with slower potential output growth.
  - Figure 2.2: presents 10-year rolling regressions of the Okun curve (∆u_t = α − β ∆Y_t).
- Regression finding:
  - The coefficient on the GDP growth rate (β) is described as "pretty stable".
  - There has been a steady downward shift in the intercept (α).
- Related identity:
  - The growth rate consistent with unchanged unemployment is α / β.

### Implications for diagnosis of weak growth
- Diagnostic distinction:
  - A slowdown attributed to weak demand would predict rising unemployment (movement along Okun curve).
  - A slowdown caused by falling potential output growth explains low GDP growth together with declining unemployment via a leftward shift of the Okun curve.
- Policy relevance:
  - Misdiagnosing a leftward shift (supply-driven slowdown) as a demand shortfall can lead to inappropriate policy responses; the section motivates later analysis of consequences when central banks treat a slowdown in potential output as cyclical.

### Model implications and key equilibrium relationships
- Equation (36): ∆ logY = n + g + α(∆ logK − (n + g))
- Example calibration from text:
  - Capital stock growth: 3 percent
  - n + g: 1 percent
  - α = 1/3
  - Resulting GDP growth: 1 2 ⁄ 3 percent.
- With capital stock growing at 3 percent and GDP at 1 2 ⁄ 3 percent, the capital-output ratio will increase.
- Predicted effects if n + g declines and interest rates fall:
  - Potential output growth will fall
  - Gross investment may or may not fall
  - The capital-output ratio will rise
  - Capital consumption will rise
  - Net investment will fall
  - Returns on capital will fall
  - Leverage will increase

### Stylized empirical findings (advanced countries)
- n + g and interest rates:
  - Working age population growth and labor-augmenting technological progress have declined; in most advanced countries labor-augmenting technological progress plus working age population growth is currently below 1 percent.
  - Both short-term and long-term interest rates have fallen, in nominal and in real terms.
- Potential output growth has fallen:
  - Japan: potential output growth slowed from 4 percent in 1990 to less than 1 percent currently.
- Gross investment:
  - Gross investment has fallen in advanced countries, with sharpest declines in Japan and relatively better performance in the euro area.
  - Example: In 1997 gross investment in Japan was still 29 percent of GDP—down only 4 percentage points from the peak in 1990.
- Capital services and capital productivity:
  - According to Penn World Database version 9.1, capital services have increased faster than GDP; capital productivity has declined.
- Capital consumption and net investment:
  - Capital consumption has increased, particularly sharply in Japan and the euro area.
  - Net investment has declined in advanced countries, most dramatically in Japan.
  - Example comparisons: Japan capital consumption around 22 percent of GDP; United Kingdom capital consumption 12 percent of GDP.
- Returns on capital:
  - The rate of return on capital has fallen in advanced countries (Penn World Tables).
  - Example: In Japan the capital income share increased by about 10 percent while the capital-output ratio increased by about one third.
- Leverage:
  - Leverage in the United States and the Euro area has increased sharply.
  - Japan experienced deleveraging after the mid-1990s banking crisis.

### Country case: Japan (illustrative)
- Policy rates reduced sharply after early-1990s land and stock market deflation.
- Investment and capital dynamics:
  - Gross investment declined only gradually; 1997 gross investment was 29 percent of GDP.
  - Capital consumption peaked at 25 percent of GDP in 2009 and remains around 22 percent of GDP, compared with 16 percent of GDP in the United States and 12 percent in Britain.
  - The capital stock increased rapidly but did not translate into rapid GDP increase; capital-output ratio rose and return on capital fell.
  - Eventually investment dropped and capital-output stopped rising; growth of capital services is now in line with growth of GDP, both at low rates consistent with low n + g.
- Okun’s law:
  - Okun’s law still holds in Japan, but the level of GDP growth consistent with unchanged unemployment has fallen sharply.

### Causality: Is low investment the cause of low growth?
- If g is exogenous and investment drops:
  - Short-run: decline in GDP growth rates
  - Long-run: decline in GDP levels
  - But lower investment with unchanged g leads to lower capital-output ratios, which contradicts observed rising capital-output ratios—suggesting causality from lower n + g to lower investment, not the reverse.
- If g depends on investment (g = g0 + λi):
  - A fall in i lowers g and GDP growth, but also lowers the capital-output ratio—again at odds with observed data.
- Conclusion from model and evidence: low investment is largely the result of low n + g rather than its cause.

### Quantitative impact of higher investment on levels
- Elasticity of balanced-growth-path output w.r.t. investment rate:
  - ∂y*/y* ÷ ∂i*/i* = α/(1 − α)
  - Example: α = 1/3 → an increase in the investment rate from 20 to 21 percent (a 5 percent increase) leads to a 2.5 percent increase in the steady state path of GDP; if accompanied by a higher saving rate, steady state consumption increases by 1.2 percent.
- Historical comparison:
  - Investment rate in advanced countries: 23.0 percent (five years ending 2007) vs 21.6 percent (five years ending 2018).
  - If investment had remained at pre-crisis ratios, steady-state-growth-path level of output would have been 3.2 percentage points higher.
  - GDP in 2018 was 12.4 percent lower than forecast in the Spring 2007 WEO—evidence that disappointing growth was not primarily due to disappointing investment but to disappointing TFP growth.

### Is investment in advanced countries “too low”?
- Argument summary:
  - Investment is lower than in the past, but this may be because n + g has fallen.
  - Raising investment without corresponding increases in TFP or working age population growth may raise capital-output ratios and reduce returns on investment.
- Cross-country examples:
  - Japan: gross investment rate ~24 percent, capital consumption ~22 percent of GDP.
  - United Kingdom: gross investment rate ~17 percent, capital consumption ~12 percent of GDP; net investment in the United Kingdom is therefore higher than in Japan, contributing to faster growth (United Kingdom ~2 percent vs Japan ~1 percent).
- Embodied technological progress caveat:
  - If technological progress is embodied, there is a stronger link between investment and productivity; embodied progress was high in the late 1990s but appears much less important today.

### The trap of prolonged low interest rates
- Prolonged low interest rates lead to:
  - High capital-output ratios
  - High capital consumption
  - Low return on capital
  - High leverage
- New equilibrium characteristics:
  - Continued high gross investment is needed just to maintain the capital stock.
  - Japan needs investment of over 22 percent of GDP just to keep the capital stock constant.
  - If interest rates rise, low-return investment will drop, capital stock growth will fall, GDP growth will drop, and NPLs may increase due to high leverage.
- Implication: a prolonged period of low policy rates may have caused a decline in the natural rate of interest rather than the natural rate causing low policy rates.

### Conclusion (summary of main arguments)
- GDP growth, investment rates, and interest rates have declined together in advanced countries.
- The decline in n + g reduced potential growth and shifted the Okun curve leftward; modest growth coincided with falling unemployment.
- Central banks misdiagnosed supply-driven slowdowns as demand-driven and responded with low policy rates; while such policy revived gross investment, it did not revive net investment or sustainable growth.
- Low policy rates contributed to higher capital-output ratios, lower returns on capital, and higher leverage—consistent with observed developments in major advanced countries.
- Policy implication: boosting investment without increases in TFP or working age population growth risks further lowering returns and raising capital consumption, rather than delivering higher growth.

*Source: wpiea2019208-print-pdf — 2.1 The leftward shift of the Okun curve*

### 2.1    The leftward shift of the Okun curve  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .   10

### 2.1    The leftward shift of the Okun curve

### Okun’s law — definition and key equations
- Okun’s law (level form):
  - u_t − u*_t = −β (Y_t − Y*_t)  (equation (1))
  - where u_t is unemployment, u*_t the NAIRU, Y_t the log of GDP, and Y*_t the log of potential GDP.
- First-difference form (assuming ∆u*_t = 0):
  - ∆u_t = β ∆Y*_t − β ∆Y_t  (equation (2))
- 10-year rolling regression specification used to track Okun dynamics:
  - ∆u_t = α − β ∆Y_t  (equation (3))

### Interpretation: movements along vs. shifts of the Okun curve
- If GDP growth (∆Y_t) slows while potential output growth (∆Y*_t) remains unchanged:
  - This generates a leftward movement along the existing Okun curve.
- If potential output growth (∆Y*_t) falls:
  - The Okun curve shifts to the left.
- Empirical implication highlighted:
  - The observed slowdown in GDP growth accompanied by falling unemployment is consistent with a leftward shift of the Okun curve driven by a slowdown in potential output growth, not solely weak aggregate demand.

### Empirical evidence and regression results
- Visual and regression evidence:
  - Figure 2.1: shows the Okun curve has shifted left, consistent with slower potential output growth.
  - Figure 2.2: presents 10-year rolling regressions of the Okun curve (∆u_t = α − β ∆Y_t).
- Regression finding:
  - The coefficient on the GDP growth rate (β) is described as "pretty stable".
  - There has been a steady downward shift in the intercept (α).
- Related identity:
  - The growth rate consistent with unchanged unemployment is α / β.

### Implications for diagnosis of weak growth
- Diagnostic distinction:
  - A slowdown attributed to weak demand would predict rising unemployment (movement along Okun curve).
  - A slowdown caused by falling potential output growth explains low GDP growth together with declining unemployment via a leftward shift of the Okun curve.
- Policy relevance:
  - Misdiagnosing a leftward shift (supply-driven slowdown) as a demand shortfall can lead to inappropriate policy responses; the section motivates later analysis of consequences when central banks treat a slowdown in potential output as cyclical.

*Source: wpiea2019208-print-pdf — 2.1    The leftward shift of the Okun curve*

### 0.09 initially.  The growth rate of the capital stock therefore slows to 3 percent

### wpiea2019208-print-pdf - 0.09 initially.  The growth rate of the capital stock therefore slows to 3 percent

### Model implications and key equilibrium relationships
- Equation (36): ∆ logY = n + g + α(∆ logK − (n + g))
- Example calibration from text:
  - Capital stock growth: 3 percent
  - n + g: 1 percent
  - α = 1/3
  - Resulting GDP growth: 1 2 ⁄ 3 percent.
- With capital stock growing at 3 percent and GDP at 1 2 ⁄ 3 percent, the capital-output ratio will increase.
- Predicted effects if n + g declines and interest rates fall:
  - Potential output growth will fall
  - Gross investment may or may not fall
  - The capital-output ratio will rise
  - Capital consumption will rise
  - Net investment will fall
  - Returns on capital will fall
  - Leverage will increase

### Stylized empirical findings (advanced countries)
- n + g and interest rates:
  - Working age population growth and labor-augmenting technological progress have declined; in most advanced countries labor-augmenting technological progress plus working age population growth is currently below 1 percent.
  - Both short-term and long-term interest rates have fallen, in nominal and in real terms.
- Potential output growth has fallen:
  - Japan: potential output growth slowed from 4 percent in 1990 to less than 1 percent currently.
- Gross investment:
  - Gross investment has fallen in advanced countries, with sharpest declines in Japan and relatively better performance in the euro area.
  - Example: In 1997 gross investment in Japan was still 29 percent of GDP—down only 4 percentage points from the peak in 1990.
- Capital services and capital productivity:
  - According to Penn World Database version 9.1, capital services have increased faster than GDP; capital productivity has declined.
- Capital consumption and net investment:
  - Capital consumption has increased, particularly sharply in Japan and the euro area.
  - Net investment has declined in advanced countries, most dramatically in Japan.
  - Example comparisons: Japan capital consumption around 22 percent of GDP; United Kingdom capital consumption 12 percent of GDP.
- Returns on capital:
  - The rate of return on capital has fallen in advanced countries (Penn World Tables).
  - Example: In Japan the capital income share increased by about 10 percent while the capital-output ratio increased by about one third.
- Leverage:
  - Leverage in the United States and the Euro area has increased sharply.
  - Japan experienced deleveraging after the mid-1990s banking crisis.

### Country case: Japan (illustrative)
- Policy rates reduced sharply after early-1990s land and stock market deflation.
- Investment and capital dynamics:
  - Gross investment declined only gradually; 1997 gross investment was 29 percent of GDP.
  - Capital consumption peaked at 25 percent of GDP in 2009 and remains around 22 percent of GDP, compared with 16 percent of GDP in the United States and 12 percent in Britain.
  - The capital stock increased rapidly but did not translate into rapid GDP increase; capital-output ratio rose and return on capital fell.
  - Eventually investment dropped and capital-output stopped rising; growth of capital services is now in line with growth of GDP, both at low rates consistent with low n + g.
- Okun’s law:
  - Okun’s law still holds in Japan, but the level of GDP growth consistent with unchanged unemployment has fallen sharply.

### Causality: Is low investment the cause of low growth?
- If g is exogenous and investment drops:
  - Short-run: decline in GDP growth rates
  - Long-run: decline in GDP levels
  - But lower investment with unchanged g leads to lower capital-output ratios, which contradicts observed rising capital-output ratios—suggesting causality from lower n + g to lower investment, not the reverse.
- If g depends on investment (g = g0 + λi):
  - A fall in i lowers g and GDP growth, but also lowers the capital-output ratio—again at odds with observed data.
- Conclusion from model and evidence: low investment is largely the result of low n + g rather than its cause.

### Quantitative impact of higher investment on levels
- Elasticity of balanced-growth-path output w.r.t. investment rate:
  - ∂y*/y* ÷ ∂i*/i* = α/(1 − α)
  - Example: α = 1/3 → an increase in the investment rate from 20 to 21 percent (a 5 percent increase) leads to a 2.5 percent increase in the steady state path of GDP; if accompanied by a higher saving rate, steady state consumption increases by 1.2 percent.
- Historical comparison:
  - Investment rate in advanced countries: 23.0 percent (five years ending 2007) vs 21.6 percent (five years ending 2018).
  - If investment had remained at pre-crisis ratios, steady-state-growth-path level of output would have been 3.2 percentage points higher.
  - GDP in 2018 was 12.4 percent lower than forecast in the Spring 2007 WEO—evidence that disappointing growth was not primarily due to disappointing investment but to disappointing TFP growth.

### Is investment in advanced countries “too low”?
- Argument summary:
  - Investment is lower than in the past, but this may be because n + g has fallen.
  - Raising investment without corresponding increases in TFP or working age population growth may raise capital-output ratios and reduce returns on investment.
- Cross-country examples:
  - Japan: gross investment rate ~24 percent, capital consumption ~22 percent of GDP.
  - United Kingdom: gross investment rate ~17 percent, capital consumption ~12 percent of GDP; net investment in the United Kingdom is therefore higher than in Japan, contributing to faster growth (United Kingdom ~2 percent vs Japan ~1 percent).
- Embodied technological progress caveat:
  - If technological progress is embodied, there is a stronger link between investment and productivity; embodied progress was high in the late 1990s but appears much less important today.

### The trap of prolonged low interest rates
- Prolonged low interest rates lead to:
  - High capital-output ratios
  - High capital consumption
  - Low return on capital
  - High leverage
- New equilibrium characteristics:
  - Continued high gross investment is needed just to maintain the capital stock.
  - Japan needs investment of over 22 percent of GDP just to keep the capital stock constant.
  - If interest rates rise, low-return investment will drop, capital stock growth will fall, GDP growth will drop, and NPLs may increase due to high leverage.
- Implication: a prolonged period of low policy rates may have caused a decline in the natural rate of interest rather than the natural rate causing low policy rates.

### Conclusion (summary of main arguments)
- GDP growth, investment rates, and interest rates have declined together in advanced countries.
- The decline in n + g reduced potential growth and shifted the Okun curve leftward; modest growth coincided with falling unemployment.
- Central banks misdiagnosed supply-driven slowdowns as demand-driven and responded with low policy rates; while such policy revived gross investment, it did not revive net investment or sustainable growth.
- Low policy rates contributed to higher capital-output ratios, lower returns on capital, and higher leverage—consistent with observed developments in major advanced countries.
- Policy implication: boosting investment without increases in TFP or working age population growth risks further lowering returns and raising capital consumption, rather than delivering higher growth.

*Source: wpiea2019208-print-pdf*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019208-print-pdf.pdf_