web.uvic.caweb.uvic.ca/~aahoque/Fall 2012 UVic/Chapter 8.docx · Web viewThis prediction comes true in the real world. ... This is the central equation of growth accounting. R

THE ECONOMIC IN THE VERY LONG RUN

Chapter 8

Economic Growth II:

Technology, Empirics, and Policy

1 Chapter 8: Economic Growth II. Fall 2012

This Chapter is about...

Incorporating technological progress in the Solow model

Policies to promote growth

Growth empirics: confronting the theory with facts

Endogenous growth model


Examples of technological progress

From 1950 to 2000, U.S. farm sector productivity nearly tripled.

The real price of computer power has fallen an average of 30% per year over the past three decades.

1981: 213 computers connected to the Internet2000: 60 million computers connected to the Internet

2001: iPod capacity = 5GB, 1000 songs.

2006: iPod capacity = 80GB, 20,000 songs.


Technological Progress in the Solow Model

Technological progress: Ability to produce more output with a given amount of capital and labour (inputs).

Here, technological progress works through improving the efficiency of labour input

Labour augmenting technological growth:Let E be defined as the efficiency of labour — as E grows, labour is more efficient.

Examples of things that influence E:– health, education– new technology (e.g., computers)


Assume:

Technological progress is labor augmented: it increases labor efficiency at the exogenous rate g: g= ∆EE

The production function as: Y=F (K , L× E)

where, L×E = the number of effective workers

Suppose, L = 100 and E = 1, then L × E = 100Technological growth gives E = 2, so L × E = 200.

Labour is 100 percent more efficient


So, the labour factor of production (effective labor, L×E ) is growing at a rate (n+g)

So, the break even investment is (d + n + g)k

consists of:

d k to replace depreciating capital

n k to provide capital for new workers

g k to provide capital for the new “effective” workers created by technological progress



Technological progress in the Solow model

Inve

stm

ent,

brea

k-ev

en

inve

stm

ent

Capital per worker, k

sf(k)

(d +n

+g ) k

k*

k = s f(k) (d +n +g)k

Now the capital accumulation:∆ k=i−(n+g+δ )k

¿ s . f (k)−(n+g+δ ) k

In the SS, ∆ k=0: s . f (k¿ )=(n+g+δ ) k¿

In steady state:

- y, k, and c, measured as per effective worker, are constant

- Y/L, K/L, and C/L are growing at the rate of technological

progress g.


Recall, Y¿ = y

In steady state: YL= y¿ .E

Since, E is growing at rate g, so is Y/L

Y, K, and C are growing at rate (n+g)

“According to the Solow model, only technological progress

can explain sustained growth and persistently rising living

standards.”

The Golden Rule:9 Chapter 8: Economic Growth II. Fall 2012

As before, the golden rule level is derived from consumption

function maximization. When c* is maximized:

MPK=δ+n+g

or, f ' (kGOLD¿ )=δ+n+g


Model’s Predictions

There were two main predictions:

a. Differences in the level of per capita income, explained in

the model by:

o differences in saving rates

o differences in population growth rates

o differences in technology growth rates

b. Differences in the growth rates of per capita income

o differences in technology growth rates


We can re-organize our assessment in terms of convergence.

Our model makes two predictions concerning convergence of

economies over time:

1. Countries with similar saving rates, technology and

population growth should converge to the same steady state

- output per person disparities disappear in the steady state

2. Under the same conditions, low income countries should grow

faster than high income countries (in the transition to steady

state)


But, if two economies have different rates of saving, and two

have different SS, then we should not expect convergence.

Instead, each economy will approach its own steady state.

The Solow model predicts the conditional convergence

countries converge to their own steady states, which are

determined by saving, population growth, and education.

This prediction comes true in the real world


Growth Accounting: Technological Change

The production function with effects of the changing

technology is: Y=AF (K ,L)

where, A is the current level of technology, called total

factor productivity.

For given levels of inputs, if A increases by 1 percent output

increases by 1 percent.


Taking log and doing the first order total derivatives:logY=logA+logF (K ,L)

dYY

=dAA

+ 1F (K , L) [F' K (K , L )dK+F 'L (K ,L )dL ]

¿ dAA

+ MPKF (K , L)

dK+ MPLF (K , L)

dL

¿ dAA

+MPK×KF(K ,L)

. dKK

+MPL× LF (K ,L)

. dLL

¿α . dKK

+ (1−α ) . dLL

+R

or, ∆YY

=α . ∆ KK

+(1−α ) . ∆ LL

+R

This is the central equation of growth accounting15 Chapter 8: Economic Growth II. Fall 2012

R is the growth in total factor productivity, which is not observable and cannot be explained by changes in inputs

R is called the Solow residual

Policy to Promote Growth

a.Evaluating the rate of saving

Use the Golden Rule to determine whether the Canadian saving

rate and capital stock are too high, too low, or about right.


If (MPK d ) > (n + g ),

Canada is below the Golden Rule steady state and should

increase s.

If (MPK d ) < (n + g ),

the Canadian economy is above the Golden Rule steady

state and should reduce s.

To estimate (MPK d ), three factors required, and for the

Canadian these are given as:

1. The capital stock is about 3 times of one year’s GDP:

k = 3 y


2. About 10% of GDP is used to replace depreciating

capital:

d k = 0.1 y

3. Capital’s income share to the GDP is 33%:

MPK ´ k = 0.33 y

Using 1 and 2, we get d =0.033, depreciation rate

Using 1 and 3, we get MPK = 0.11

So, for the Canadian economy MPK d = 0.077

Since 1950, the real GDP in Canada has grown at just under 4

percent per year. As such, (n + g)= 0.04

That is, (MPK d ) > (n + g )18 Chapter 8: Economic Growth II. Fall 2012

7.7% 4%

The capital stock in Canada is well below the Golden Rule

Level

Suggests saving/investment should be increased

Increase capital formation has been a high priority of

the Canadian economic policy

b.How to increase the saving and investment

Reduce the government budget deficit (or increase the budget

surplus).

Increase incentives for private saving:


reduce capital gains tax, corporate income tax, estate tax

as they discourage saving.

replace federal income tax with a consumption tax.

expand tax incentives for IRAs (individual retirement

accounts) and other retirement savings accounts


c. Encouraging technological progresses

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 theory

Solow model:

sustained growth (long-run) in living standards is due

to technological progress.

the rate of technological progress is exogenous.

Endogenous growth theory:

a set of models in which technological change is

treated as endogenous. At a general level, these are

theories that model the process of creating,

disseminating, and using ideas (new technology)


Simple AK Model

A Basic Model:

No labour input, just capital.

Let, the Production function:

Y = A K

where, A is the amount of output for each unit of capital

(A is exogenous & constant)

Key difference between this model & Solow: MPK is

constant here, diminishes in Solow


Investment: sY

Depreciation: δK

Equation of motion for total capital: ∆ K=sY−δK

Dividing the capital accumulation function both side by K, and use Y=AK we get:

∆ KK

= s (AK )K

−δ

Or, ΔKK

= ΔYY

=sA−δ

If sA>δ, then income will grow forever, and investment is

the “engine of growth”.

Here the permanent growth rate depends on s. In

Solow model, it does not.

Does Capital have diminishing returns or not?


Depends on 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 constant returns to capital is more plausible,

and this model may be a good description of economic

growth.


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web.uvic.caweb.uvic.ca/~aahoque/Fall 2012 UVic/Chapter 8.docx · Web viewThis prediction comes true in the real world. ... This is the central equation of growth accounting. R