Growth II Flashcards
How can we decompose GDP per capita?
What is it in mathematical terms?
› GDP per capita depends on
• the share of the population that is employed (”Employment/population ratio”)
• the output per person employed (”labour productivity – per worker”)
› In mathematical terms: Y/N=E/P*Y/E
Y = Output (GDP) P = Population (persons) E = Number of persons employed (=number of workers) H = Annual working hours per person employed (=per worker)
How can we split up output per person?
Output per person can be split further into:
- hours worked per worker
- output per hour worked (labour productivity per hour)
Y/E=HY/(HE)
Hence
Y/P=E/PHY/(H*E)
Describe the historical trend of GDP per capita
Historical trends:
• Male LFP (labour force participation) decreasing, female LFP increasing
• Annual working hours decreasing
› Some of the improvements have been allocated to fewer working hours as more leisure could be afforded
Explain why the fundamental driver of improvement in living standard is improvement in labour productivity
› Labour force participation and working hours:
• have natural upper bounds -> long-run impact on growth is limited
• have in fact not changed much since 1990
› Consequence: Fundamental driver of improvement of living standard is improvement in labour productivity
Describe three drivers of labour productivity
- investment in real capital (more and higherquality machinery)
- human capital (quality of labor input)
- overall productivity improvements (“technological progress”)
Describe the aggregate production function
𝑌=𝐹(𝐾,𝑁)
• Aggregate output 𝑌 (real GDP)
• K = capital input, N = labour input
• State of technology, 𝐹
F depends on
- Blueprints -> range of products that can be produced + available production techniques
- The way the economy is organized (legal institutions, political system)
What is meant by constant returns to scale?
We assume the aggregate production function has constant returns to scale
If we double input of labor and capital we also double the production
Change by the same percentage
xY=F(xK, xN)
Even under constant returns to scale, there are decreasing returns to each factor, keeping the other factor constant, why?
Decreasing marginal product for each factor (decreasing returns to capital or decreasing returns to labor)
If we only increase labor we will still produce more but not as much
The law of diminishing marginal productivity states that while increasing one input and keeping other inputs at the same level may initially increase output, further increases in that input will have a limited effect and will eventually have no effect, or a negative effect, on output.
Increases in capital lead to smaller and smaller increases in output
Increases in labor, given capital, lead to smaller and smaller increases in output
What are the two sources of growth in Y/N?
Capital accumulation - increases in K/N
Technological progress - shift the production function F - more output per worker given capital per worker
Sustained growth requires sustained technological progress. Why?
Growth in K/N can only lead to short to medium term growth
• Increases in K/N are driven by investments
• In the closed economy, investments = savings
• A higher savings rate leads to higher K/N, which initially increases Y/N
• But due to decreasing returns to K/N, more and more K/N is needed to maintain constant growth in Y/N
• Moreover: Each year, a fixed fraction of the capital stock depreciates
• Savings rate needs to become higher and higher (and cannot become larger than 100%, at which point there would be zero consumption)
• A one-time increase in the savings rate only leads to a higher level of Y/N, but not to sustained growth
In other words:
- Investment is the driving force
- We need more and more capital per worker to maintain the growth or increase the growth
- We need ever increasing capital investments per worker
- Eventually, all income goes into savings (most extreme case) - nothing left for consumption
Without technological progress: In the long-run, output per worker(Y/N) will stay constant and be produced at a constant capital/labor relationship (K/N)
Only successive technological progress allows for sustained economic growth!
Describe the function of growth accounting
Growth accounting tries to determine where the growth came from
Growth accounting decomposes observed growth into:
• growth in all factor inputs (such as capital and number of workers)
• growth due to increase in technology
Growth accounting does not explain why factor input or technology changes
• simply try to divide credit for observed output growth into its proximate sources, based on the observed growth rates in inputs
Note: capital accumulation alone cannot support sustained growth, but with technological progress, capital becomes more productive and will rise as well
What can explain growth in output (according to growth accounting)?
Growth in output is explained by
• Growth in labour input
• Growth in capital input
• Growth in productivity, TFP growth Δ𝐴/𝐴= all other (residual) factors that explain growth in output
What is the starting point for growth accounting for output Y? Describe the cobb douglas function
Starting point: aggregate production function 𝑌=𝐴∗𝑓(𝐾,𝑁) • Y= output (value added), K=capital input, N=labour input (workers), A=total factor productivity
- Cobb-Douglas production function: 𝑌=𝐴𝐾^𝛼𝑁^𝛽
- Assume𝛼+𝛽=1 and 0
Explain total factor productivity
Total Factor Productivity (TFP)
• proportion of output not explained by the amount of inputs used in production
• level is determined by how efficiently and intensely the inputs are utilized in production
• “a measure of our ignorance“
• TFP growth can be computed as the “Solow-residual”
How does growth in labour productivity (LP) and growth in TFP relate to each other?
LP growth = TFP growth + Capital income share ×Capital per worker growth
LP assigns all output growth to labour, including growth due to accumulation of capital per worker
-> LP growth > TFP growth, unless capital stock per worker declines
