Chapter 9: Economic Growth II - Technology, Empirics, and Policy

Possible explanations for positive correlation between capital per worker (K/L) and production efficiency (A)

- rising production efficiency encourages further capital accumulation - capital accumulation generates non-rival "externalities" that raise efficiency - capital accumulation raises income per worker, taxes, and supports higher levels of social infrastructure: quality of governments, regulations, and institutions

Saving and Investment per Effective Worker

s y = s f(k)

Policy Issues: Evaluating the Rate of Saving Relative to the Golden Rule

use the golden rule to determine whether the U.S. saving rate and capital stock are too high, too low, or about right recall: the MPK is the slope of the production function [y = f(k)], which is convex and has a decreasing slope as you move away from the origin recall: The Golden Rule state is achieved when the slope of the production function [=MPK] equals the slope of the diagonal break even investment line [= δ + n + g] - If (MPK − δ) > (n + g), the U.S. economy is below the Golden Rule s. state and should increase s. - If (MPK − δ) < (n + g), the U.S. economy is above the Golden Rule s. state and should reduce s. to estimate (MPK − δ), use three facts about the U.S. economy from the statistics published by the Bureau of Economic Analysis on GDP and the capital stock

Technological Progress in the Solow Model: The E Factor

we now write the production function* as: Y = F(K,L x E).....Y = A*F(K,L) = (AK)^a(LE)^1-a L x E = number of effective workers E = output per worker (efficiency of labor) technological progress equals productivity growth Y/L grows at the rate of productivity growth

Conditional Convergence

what the Solow model really predicts is conditional convergence: - countries converge to their own "steady states": s, n, g - steady states are determined by saving, population growth, and technical progress this prediction comes true in the real world

y

y = Y/LE = output per "effective" worker

Production Function per Effective Worker

y = f(k)

Δk

Δk = sf(k) - (δ + n + g)k investment (sf(k)) - break-even investment ((δ + n + g)k)

Difference in income per capita (or "steady states") among countries can be due to differences in

1. Capital accumulation (physical capital or human capital) per worker (K/L) 2. the efficiency production (A), or technology 3. the quality of the labor force (L) - cumulative years of education

3 facts about the U.S. economy from the statistics published by the Bureau of Economic Analysis on GDP and the capital stock (that can be used to estimate MPK - δ

1. k = 2.5y .... the capital stock is about 2.5 times one year's GDP 2. δk = 0.1y ... About 10% of GDP is used to replace depreciating capital (recall "capital consumption allowances" = economic depreciation) 3. MPK × k = 0.3y ... Capital income is about 30% of GDP.

Facts about R&D

1. much research is done by firms seeking profits 2. firms profit from research - patents potentially create a stream of monopoly profits - there is potentially "excess profit" or rent, in being first on the market w/ a new product 3. innovation combined w/ industry "locational clustering" produces "externalities" that reduce the cost of subsequent innovation

Convergence

Solow model predicts that, other things equal, poor countries (w/ lower Y/L and K/L and lower capitalization) and thus higher MPK relative to [δ + n + g] should grow faster than rich ones if true, then the income gap between rich and poor countries would shrink over time, causing living standards to converge if economies have different steady states, then we should not expect convergence (each economy will approach its own steady state)

Endogenous Growth Theory

Solow model: - sustained growth in living standards is due to technological progress - the rate of technological progress (g) is "exogenous" in Endogenous growth theory: - the growth rate of productivity and living standards in "endogenous" - by "endogenous", it implies that key drivers of the rate of technological progrss (g) can be influenced by policies, regulations and institutions - "semi-endogenous": that growth rates may be impacted by policies temporarily, but the economy eventually converges to an exogenous steady state

The Efficiency of Production (A) or Technology

Y = A*F(K,L) = AK^αL^1-α A = the "height" of the production function, or "multifactor productivity", or "Hick's neutral technical progress"

Y grows at rate g + n

Y = y(E x L) = (YE) x L the growth rate of Y = the growth rate of (yE) plus that of L in the steady state, the growth rate of (yE) equals g we assume that L grows at rate n

Policy Issues: Establishing the Right Institutions

creating the right institutions is important for ensuring that resources are allocated to their best use...examples: legal institutions, to protect property rights capital markets - financial capital flows to the "best" investment projects - price risk vs. return efficiently - prevent fraud and insider trading a corruption-free government, to promote competition, enforce contracts, etc.

g

g = ΔE/E because the labor force L is growing at rate n, and the efficiency of each unit of labor E is growing at rate g, the effective number of workers is growing at rate n + g

Policy Issues: Allocating the Economy's Investment (3 categories of capital)

in the Solow model, there's one type of capital (physical capital), but in the real world, there are many types, which we can divide into 3 categories 1. private capital stock (per the Solow model) 2. public infrastructure 3. human capital: the knowledge and skills that workers acquire through education and accumulated experience

Income per capita and capital per capita in the Solow model

income per capita: y = (Y/L) is constant in the steady state capital per capita: k = (K/L) is constant in the steady state neither point is true in the real world

Does capital have diminishing returns or not?

it depends on the definition of capital if capital is narrowly defined (only plant and equipment), then yes advocates of endogenous growth theory argue that "knowledge" is a type of capital If so, then Romer-esque constant returns to capital factor A is more plausible, and this model may be a good description of economic growth.

Assume: Technological progress is labor-augmenting (i.e. raises productivity per worker)

it increases labor efficiency/productivity at a trend exogenous rate g

k

k = K/LE = capital per "effective" worker

Technological Progress (g) in the Solow Model

net investment per worker = gross investment per worker - depreciation of capital per worker - growth new workers*k - growth of new virtual (robotic) workers*k Δk = s f(k) − (δ +n +g)k now that k is defined as the amount of capital per effective worker, increases in the effective # of workers bc of technological progress tend to decrease k...in the steady state, investment sf(k) exactly offsets the reductions in k attributable to depreciation, population growth, and technological progress capital per effective worker k is constant in the steady state and because y=f(k), output per effective worker is also constant

Policy Issues: Evaluating the Rate of Saving Conclusion

net marginal product of capital = MPK - δ = 0.08 U.S. real GDP grows an average 3% per year, so n + g = 0.03 thus, MPK - δ = 0.08 > 0.03 = n + g conclusion: the U.S. is below the Golden steady state...increasing the U.S. saving rate would increase consumption per capita in the long run

In the real world, many poor countries do not grow faster than rich ones. Does this mean the Solow model fails?

no because it predicts that, other things equal, poor countries (w/ lower Y/L and K/L) should grow faster than rich ones

Efficiency of Labor (E variable)

output per worker; level of labor productivity increases in labor efficiency E (productivity) = increases in the (effective) labor force as the available technology improves, E rises, and each hour of work contributes more to the production of goods and services E also rises when there are improvements in the health, education or skills of the labor force ex. cars per day per worker

Policy Issue: Encouraging Technological Progress

patent laws: encourage innovation by granting temporary monopolies to inventors of new products tax incentives for R&D grants to fund basic research at universities industrial policy: encourages specific industries that are key for rapid technological progress (subject to the preceding concerns)

Endogenous Growth: A basic "AK" Romer Model

production function: Y = AK - Y = A*F(K,L) = AK^αLE^1-α = output - a = 1 K = capital stock - A = the amount of output produced for each unit of capital (A is exogenous and constant) - Increasing returns to scale: double inputs, 2A and 2K, then 4Y [more than double output] key difference between this model and Solow: - MPK = dy/dk = A - MPK = the slope of the production function = constant - Contrast with diminishing returns in Solow model (the famous α exponents) - Recall: the slope of the production function decreases with higher capital per worker, or higher capital per effective worker (Solow) investment: sY depreciation: δK Same equation of motion for capital accumulation: ΔK = sY − δK = investment - depreciation ΔY/Y = ΔK/K = sA - δ in this model, saving and investment can lead to persistent growth

Policy Issues: How to Increase the Saving Rate

reduce the government budget deficit (or increase the budget surplus) increase incentives for private saving: - reduce capital gains tax, corporate income tax, and estate tax, as they discourage saving - replace federal income tax w/ a consumption tax - expand tax incentives for IRAs (individual retirement accounts) and other retirement savings accounts

A Two-Sector Model w/ Specialized Research Workers: Key Variables

s: affects the level of income but not its growth rate (same as in the Solow model) u (share of labor force involved in research production): - Impacts the level of income (inversely correlated, as a higher u implies fewer production workers) - And growth rate of income (positively correlated).

Endogenous Growth: if sA > δ

savings (s) is the engine of growth output (Y) will grow proportionately if sA > δ, the economy's income grows forever, even w/o the assumption of exogenous technological progress

Technological Progress in the Solow Model: Total Output (symbol and steady-state growth rate)

symbol: Y = y × (E × L) steady-state growth rate: n + g

Technological Progress in the Solow Model: Output per Worker (symbol and steady-state growth rate)

symbol: Y/L = y × E steady-state growth rate: g (productivity)

Technological Progress in the Solow Model: Capital per Effective Worker (symbol and steady-state growth rate)

symbol: k = K/(E × L) steady-state growth rate: 0 (definition of new steady state)

Technological Progress in the Solow Model: Output per Effective Worker (symbol and steady-state growth rate)

symbol: y = Y/(E × L) = f(k) steady-state growth rate: 0 (k is constant)

Sustained Growth and Living Standards

technological progress can lead to sustained growth in output per worker but contrast, a high rate of saving leads to a high rate of growth only until the steady state is reached once the economy is in steady state, the rate of growth of output per worker depends only on the rate of technological progress according to the solow model, only technological progress can explain sustained growth and persistently rising living standards

Balanced Growth

the Solow model's steady state exhibits balanced, or steady state growth: many variables grow at the same rate in the steady state model predicts that Y/L and K/L grow over time at the same rate (g), so K/Y = (K/L)/(Y/L) should be constant, i.e. d(K/Y)/dt = 0....this is true in the real worlds model predicts that real wage grows at the same rate as output per worker: d(Y/L)/dt = g = productivity growth = growth in the marginal product of labor = real wage growth model predicts the real rental price of capital (MPK) is constant = δ + n + g....also true in the real world

Break-Even Investment

the amount of investment necessary to keep k (now capital per effective worker) constant, given the rate of productivity growth, g break-even investment = (δ + n + g) x k = the amount of investment necessary to keep k (now capital per effective worker) constant. consists of: - δ k to replace depreciating capital - n k to provide capital for new workers - g k to provide capital to "operationalize" technological progress

Y/L and K/L grow at rate g

the definition of y implies (Y/L) = yE the growth rate of (Y/L) = the growth rate of y plus that of E in the steady state, y is constant, while E grows by definition at rate g K/L = kE and in the steady state, k is constant, while E grows by definition at rate g, so the growth rate of (K/L) = g

The Golden Rule w/ Technological Progress

the golden rule level of capital is now defined as the steady state that maximized consumption per effective worker c* = f(k*) - (δ + n + g)k* steady-state consumption is maximized if MPK = δ + n +g or MPK - δ = n + g

Possible Problems w/ Industrial Policy

the gov. may not have the ability to "pick winners" (choose industries w/ the highest return to capital or biggest externalities) politics rather than economics may influence which industries get preferential treatment may lead to unintended higher concentration across industries

"Hybrid" Growth Model

the growth of technical progress (g) is an additive factor to population growth n...the population of workers and research ideas combined is growing at (n+g)...you still have to add depreciation, δ, which now applies to the entire capital stock

Basic AK Romer endogenous growth model:

the long term growth rate depends on s Contrast with Solow model: population growth & technological progress, savings does not impact steady state growth, but only the level of capital/effective worker

Saving Rate

the saving rate determines the steady-state levels of capital and output one particular saving rate produces the golden rule steady state, which maximizes consumption per worker and economic well-being

A Two-Sector Model w/ Specialized Research Workers

two sectors: - firms produce goods and services - research universities, institutes and labs "produce" research/innovation workers that increase labor efficiency in the production of goods and services u = fraction of labor force in research (u is exogenous); 1-u is the fraction in manufacturing E = the stock of knowledge g = function that shows how the growth in knowledge depends on the fraction of the labor in universities Research (or ideas) production function: - ΔE /E = g = g(u) - Productivity growth is a function of the fraction of labor force in research production function: Y = F [K, (1 − u )E L] capital accumulation: ΔK = s Y − δK In the steady state, manufacturing output per worker and the standard of living grow at rate: ΔE / E = g (u).

Policy Issues: Allocating the Economy's Investment (how should we allocate investment among the 3 categories of capital?)

two viewpoints: 1. equalize tax treatment of all types of capital in all industries and let the market allocate investment to the type w/ the highest marginal product 2. industrial policy: government should actively encourage investment in capital of certain types or in certain industries because it may have positive externalities that private investors don't consider