Productivity and Growth

Graph of potential GDP and actual GDP. Actual dipped during the great depression, but went above the line during and after WW2.

Used logarithmic scale to create a linear graph, but the actual graph is exponential. Rapid growth or decline is even more dramatic in reality.

Rule of 70:

Number of years to take to double in size = 70/annual growth rate (in percent)

Example: If an economy grows at 2% each year, then it would take about 35 years to double. or equivalently, every 35 years it would double. If this economy grew just 1 percentage point faster, at 3% each year, then it would take just 23 years to double.

Einstein called the discovery of the power of compounding is the greatest discovery.

Growth and Living Standards

What matters for living standards is per capita GDP = GDP/population

Let Z=X/Y

Then %dZ = %dX - %dY

Therefore, %d percapita GDP = GDP growth (3.09%) - population growth (1.27%)

What drives our standard of living? Is per capita GDP a perfect measure of living standards?

How about crime, pollution, the beauty of the landscape, income distribution across the population? Nonetheless, GDP per capita is the best measure of economic well-being for practical reasons.

The key is labor productivity. So the question is: what drives labor productivity growth?

Power of compounding:

In 1870, UK GDP per capita > US GDP per capita by 18%

In 1990, US GDP per capita > UK GDP per capita by 50%

This dramatic shift in living standards came about with less than 0.5% difference! In 1870-1990 UK growth rate of per capita GDP - 1.37%, US growth rate - 1.85%.

In 1950, UK GDP per capita > German GDP per capita by 57% (due to WW2)

In 2000, German GDP per capita > UK GDP percapita by 3%

It came from 1% point difference in growth.

Growth Accounting Equation

Y = AxF(K,L)

The production function can be influenced either by increasing capital K or labor L. The technology (overall efficiency) factor A might also go up, which would increase output Y.

Corruption diverts the talents and resources from improving overall efficiency A. This is what is causing several Latin American countries from maximizing output despite an abundance of capital stock K and human resources L.

A is also called TFP = total factor productivity.

See Mankiw (p 244) for the derivation of the growth accounting equation.

Y = AxF(K,L) ~ production function (level form)

How do we express this in terms of % change?

%dY = %dA + α%dK + (1-α)%dL

where

α = capital income share = 0.3 in US

1-α = labor income share = 0.7 in US

This equation can be used to explain the percentage contribution of each factor to the overall output growth. See table 1 in the handout. Surprisingly, TFP declined in 70s and 80s. Labor growth grew due to the baby boomers, women and teenagers entering the labor market.

Labor Productivity: The Key to Rising Living Standards

Productivity of labor = Y/L (the quantity of output per unit of labor)

Consider living standard as measured by Consumption/person.

Assume consumption is only some %age of total output: C = (1-s)Y, where s = savings.

Then,

C/person = (1-S)(Y/person) = (1-s)(L/person)(Y/L), where L is labor.

How can we increase C/person?

(i) reduce S (savings rate). but this is at a cost of future consumption. (Recall S=I, therefore S down leads to I down leads to K down leads to future consumption down)

(ii) raise (L/person) - the labor participation ratio. But this is not always desirable. It's limit to 100%. It comes at the expense of leisure time.

(iii) raise (Y/L) - labor productivity. This is the key!

See Paul Krugman's Age of Diminished Expectations. He understood this.

What determines labor productivity growth?

Recall: %dY = %dA + α%dK + (1-α)%dL

Let's rewrite this in terms of %d(Y/L) = %dY - %dL

So %dY/L = %dA + α%dK + (1-α)%dL - %dL

= %dA + α%dK + -α%dL

Regrouping,

= %dA + α(%d(K/L))

K/L is capital stock per worker

So labor productivity can be improved by:

(i) increasing K/L - capital stock per worker. This explains why well-equipped Americans have higher productivity than poorly-equipped African workers.

We can achieve K up through increasing I. Recall that S=I, so increase I by encouraging increasing savings, S.

Feldstein-Horioka puzzle found that S and I move closely together as if they're in a closed economy.

S^{g} is the fiscal burden from population aging.

Social Security benefit is a pay-as-you-go/funded program. Elders are paid as young ones are paying.

(ii) increase productivity A

1 - one way to increase productivity is to improve the inputs through education and training - investment in human capital. A year of schooling tends to increase income by 8%. MBA, even more so. :)

2 - another way to do increase productivity is to improve production technology

See Table 2 in handout (page 8).

Rapid productivity growth in US in 60s, but then it fell for 3 decades due to falling TFP and captial per worker.

## Wednesday, April 30, 2008

### Lecture 5 - Productivity and Growth

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