What do we know about the causes of regional growth?

ECON 4480 State and Local Economies

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Defining growth• But first, we should be clear about how to

define growth.• Typically, one or more of the following

measures are used:• Growth of output,• Growth of output per worker, and• Growth of output per capita.

• The ‘right’ measure depends on the issue we are investigating.

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Defining growth•Output growth is a measure of the growth of productive capacity,•Growth of output per worker measures productivity growth, which is a primary indicator of a region’s competitiveness, and•Growth of output per capita is a good measure of changes in economic welfare (more output per capita means more consumption of output per person).•All three measures are useful; there is no ‘best’ measure of growth.

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Summary Facts

• Measures of competitiveness and economic welfare vary substantially across regions.

• Growth rates of capacity, competitiveness and economic welfare differ greatly across regions.

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Regional Status 2011

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Regional Snapshot 2011

• Competitiveness (output per worker): • High: New England, Mideast, Far West• Low: Plains, Southeast

• Economic Welfare (output per capita): • High: New England, Mideast, Far West• Low: Plains, Southeast, Rocky

Mountain

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Regional growth rates

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Measures of Growth 1970-2011• Growth of Capacity (output):

• High: Southwest, Rocky Mountain• Low: Great Lakes, Mideast

• Growth of Competitiveness (output per worker): • High: New England, Plains, Southwest• Low: Great Lakes, Plains

• Growth of Economic Welfare (output per capita): • High: New England, Southwest• Low: Great Lakes, Far West

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Theories of Growth

– Neoclassical growth theory,– Demand-side models (Keynesian), and– Cumulative causation models,

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Neoclassical growth theory

• Emphasizes supply-side variables such as labor and capital.

• Case 1: Growth with no technical change• Output (Y) depends on Labor (L) and Capital (K)• Equation: Y = f ( L, K)• Labor is defined as employment or the labor force.• Capital is the stock of equipment, tools, machines,

and structures at a given point in time.• Output grows only when L and/or K grow.

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Neoclassical Theory

• Divide both sides by L and we have:– Y / L = f( K / L) , an equation for productivity.– This tells us that the only way we can increase

productivity is to grow the amount of capital stock per worker.

– In other words, capital stock must grow faster than labor supply in order for productivity to grow.

– The relationship is shown in the graph (next).

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Output per worker

Capital per worker (K/L)

Productivity (Y/L) Y/L = f(K/L)

K/L0

• Productivity is determined by the amount of capital per worker.

• Productivity will rise as K/L rises, but at a diminishing rate.

• Rising K/L is called capital deepening.

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Y/L0

Digression: Why is productivity important?

• Productivity and average pay are strongly linked: states with the highest productivity also enjoy the highest wage rates.

• The relationship between productivity and average pay is a long-run relationship.

• To increase average pay, a state must figure out how to increase productivity.

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Evidence: Productivity and Average Pay

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Evidence: Productivity and Average Pay

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Productivity and pay

• Conclusion: average pay is strongly tied to productivity.

• Increase productivity and higher average pay should follow.

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Productivity and pay• Using the 50 state model, a $1,000 increase in

productivity will raise average pay by $1,000 * 0.5468 = $547.

• Average pay for the median state is $48,816, while Tennessee’s average pay is $47,828, a difference of $988.

• We estimate that making up the $988 difference would require an increase in Tennessee productivity of $1,807 ($988/0.5468).

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Productivity Ranking

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Average Pay Ranking

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Cobb-Douglas• We can express the output relationship more

specifically in the Cobb-Douglas format: Y = A Kα Lβ (1)

• Where ‘A’ is a constant, ‘α’ is the contribution of capital to output, and ‘β’ is the contribution of labor to output.

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Cobb-Douglas• If α + β =1, then the production function

exhibits constant returns to scale.• Assuming constant returns, the production

function becomes Y = A Kα L 1-α

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Output Growth Equation• Applying some matha to equation (1), we can

derive the output growth equation: ΔY/Y = α ΔK/K + (1-α) ΔL/L (2)

• The symbol delta (Δ) means ‘change in’, so ΔY/Y is the percent growth rate of output. Similarly for capital and labor.

• Equation (2) says that output growth is a weighted average of the growth rates of capital and labor.

• aTake logs of both sides and differentiate with respect to time.

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Output Growth Equation• Specific example: Suppose capital grows by

5% and labor grows by 1%. Assume α=0.4. then the growth rate of output is: ΔY/Y = α ΔK/K + (1-α) ΔL/L ΔY/Y = 0.4(.05) + (0.6)(.01) ΔY/Y = 0.026 = 2.6%

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Productivity Growth Equation• If we subtract ΔL/L from both sides of equation (1)

the result is the productivity growth equation: ΔY/Y - ΔL/L = α (ΔK/K - ΔL/L) (3)

• Productivity growth is the excess of output growth over labor growth (left-side).

• Productivity growth accelerates when capital is growing faster than labor (right-side).

• Capital stock must grow faster than labor force if productivity is to grow (assuming no technical change).

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Productivity Growth Equation

• Specific example: suppose capital is growing by 5%, labor by 1%, and α=0.4. Productivity growth is ΔY/Y - ΔL/L = α (ΔK/K - ΔL/L) ΔY/Y - ΔL/L = 0.4(.05-.01) ΔY/Y - ΔL/L = 0.016 = 1.6%

• Productivity rises by 1.6% per year.

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Neoclassical Theory

• Summary for Case 1: No Technical Change– Output will rise without limit as long as both K and

L rise.– Output per worker will rise only if there is capital

deepening (K/L is rising).– Growth in productivity ends when the

capital/labor ratio reaches a long-run equilibrium. Capital deepening has limits.

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Neoclassical Theory

• Limit to Case 1:– At some point in time, for a given amount of

labor, additional capital will not generate additional output (growth).

– Beyond this long-term equilibrium point, additional capital will increase the capital/labor ratio, but does NOT increase output.

– Labor productivity growth is reduced to zero. – Capital deepening has limits.

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