What do we know about the causes of regional growth? ECON 4480 State and Local Economies 1

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. 2

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. 3

Summary Facts Measures of competitiveness and economic welfare vary substantially across regions. Growth rates of capacity, competitiveness and economic welfare differ greatly across regions. 4

Regional Status

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 6

Regional growth rates 7

Measures of Growth 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 8

Theories of Growth – Neoclassical growth theory, – Demand-side models (Keynesian), and – Cumulative causation models, 9

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. 10

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). 11

Output per worker Capital per worker (K/L) Productivity (Y/L) Y/L = f(K/L) K/L 0 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. 12 Y/L 0

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. 13

Evidence: Productivity and Average Pay 14

Evidence: Productivity and Average Pay 15

Productivity and pay Conclusion: average pay is strongly tied to productivity. Increase productivity and higher average pay should follow. 16

Productivity and pay Using the 50 state model, a $1,000 increase in productivity will raise average pay by $1,000 * = $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). 17

Productivity Ranking 18

Average Pay Ranking 19

Cobb-Douglas We can express the output relationship more specifically in the Cobb-Douglas format: Y = A K α L β (1) Where ‘A’ is a constant, ‘α’ is the contribution of capital to output, and ‘β’ is the contribution of labor to output. 20

Cobb-Douglas If α + β =1, then the production function exhibits constant returns to scale. Assuming constant returns, the production function becomes Y = A K α L 1-α 21

Output Growth Equation Applying some math a 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. a Take logs of both sides and differentiate with respect to time. 22

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 = = 2.6% 23

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). 24

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( ) ΔY/Y - ΔL/L = = 1.6% Productivity rises by 1.6% per year. 25

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. 26

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. 27