research methods in macro

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Copyright © 2013 Pearson Education, Inc. Publishing as Addison-Wesley

PHYSICAL

CAPITAL

Chapter 3

Marco Savioli




Physical capital

Capital: physical objects that extend our ability or dowork for us

Capital includes

Machines

Buildings

Infrastructure (roads, ports, vehicles)

Raw materials

The worker who has more or better capital to workwith will be able to produce more output




3-3

Figure 3.1 GDP and Capital per Worker, 2009




The nature of capital

Capital is productive: raises workers’ productivity

Capital is produced: difference with natural resources,through less consumption → investment (saving)

Capital is limited: it is rival , ideas (investment is R&D)differ from capital in that infinite people can use them

Capital can earn a return: because it is productiveand its use is limited, incentive for capital creation

Capital wears out: depreciation because of using orthe passage of time




Production function

Express the relationship between inputs (factors ofproduction) and the amount of output produced

= (, )

Constant returns to scale

(, ) = (, )

1

=

1

, =

,

=

, 1

= , 1 = ()




3-6

Figure 3.2 A Production Function with

Diminishing Marginal Product of Capital

=(, )

=()




Cobb-Douglas productionfunction

Does a good job of fitting data on inputs and outputs

(, ) = −

measures productivity, 0 < < 1 determines how

capital and labor combine to produce output

=

=

(, )

=

,

=

−

=




Cobb-Douglas productionfunction

Constant return to scale

, = − = +− − = (, )

=

= −−

Diminishing marginal product:

= 1 −2− < 0




3-9

Figure 3.3 Capital’s Share of Income in a

Cross-Section of Countries

Knowingcapital’s share

of nationalincome willtell us thevalue of ifthe productionfunction is aCobb-Douglas

There is nosystematic

relationshipbetweencapital’s shareof nationalincome andGDP percapita




Factor payments and factorshares in a Cobb-Douglas p.f.

= −−

In a competitive economy, the marginal product of capitalwill equal the rental rate per unit of capital

Total amount paid out to capital will equal ×

′ ℎ = ×

=

−

− =

′ ℎ = 1

Even though the quantities of capital and labor in the

economy may vary, the shares of national income paid outto each factor of production will be unaffected




Determination of capital perworker

In this version of the Solow model, we assume thatthe quantity of labor input, L, is constant over time

We also assume no improvement in productivity, A

Δ =

Δ =

We assume that a constant fraction of output isinvested and that a constant fraction of the capitalstock depreciates each period

Δ = = ()




3-12

Table 3.1 Agricultural Land as a Fraction of

Total Wealth in the United Kingdom

Before the19th century,the mostimportantfactor ofproductionother thanlabor was land

Decline inland as afraction of

total wealthmirrorsdecline inpayments

Because ofchanges intechnology(industrialrevolution)capitalreplaced landas a key input

«Postindustrial» economy:knowledge

and skillsreplacephysicalcapital




Measuring change over time

Two ways to measure how something changes overtime

How much it changes between one year and the next,difference:

Δ = +

Change in a variable relative to its initial value,growth rate:

=Δ

In continuous time: =

, =




3-14

Figure 3.4 The Steady State of the Solow

Model

Δ = ()

→ →

= steady-statecapital stock, theamount of capitalper worker will notchange over time

The steady-state,in this case, isstable




3-15

Figure 3.6 Effect of Increasing the Investment

Rate on the Steady State

Increasing , thefraction of outputinvested, from to2

An increase in ,

the rate ofdepreciation, wouldlead to lowersteady-state levelsfor capital andoutput




Figure 3.10 Speed of Convergence to the

Steady State - Cobb-Douglas p.f.

Δ =

=Δ

= −

The growth rate ofcapital is larger, the

further below its

steady state a country

is




Steady states

Using the Cobb-Douglas p.f., =

Δ =

Steady state:

0 =

=

(−)

=

= /(−)

(−)




The Solow model as a theory ofincome differences

Consider two countries (i and j )

= /(−)

(−)

= /(−)

(−)

=

(−)




3-19

Figure 3.7 Predicted versus Actual GDP per

Worker

There issome

relationshipbetweenactual andpredictedincome, butnot a strongone

Otherinfluencesoncountries’income:populationgrowth,otherfactors ofproduction,productivity

Countriesmight notbe in theirsteady state




The Solow model as a theory ofrelative growth rates

Once a country reaches its steady state, there is no longer anygrowth!

All of the growth that we observe in this model will betransitional (to a steady state)

A country far below steady state will grow quickly

Convergence toward the steady state: a country’s per-workeroutput will grow or shrink toward the SS

If two countries have the same rate of investment, the countrywith lower income has higher growth (but same )

If two countries have the same level of income, the country witha higher rate of investment has higher growth (different )

A country that raises its level of investment experiences anincrease in its rate of income growth




The relationship betweeninvestment and saving

Solow model: differences in investment rates lead todifferent steady states

Every act of investment corresponds to an act ofsaving

Building capital requires the use of resources thatcould otherwise have been used for something else

Investment can cross national borders

Although international flows of investment can be

important at times, the most significant determinantof a country’s investment rate is its own saving rate




3-22

Figure 3.8 Saving Rate by Decile of Income

per Capita




Explaining the saving rate:exogenous vs endogenous factors

Endogenous variables: determined within the model

Exogenous variables: are taken as given in the model

If saving is exogenous countries differ in saving ratesfor reasons that are unrelated to their level of income

per capita

Saving rate may differ because of fundamentaldeterminants like government policy, incomeinequality, culture and geography

If saving is endogenous rich countries save more, butsaving more does not make a country rich




The effect of income on saving

In poor countries people simply «can’t afford to save» This argument fails for even slightly richer countries

Saving represents a choice between current and futuresatisfaction. A person who does not care much about thefuture will not save

Poor countries have lower saving rates than rich ones

Assumption =

< 2

=

< ∗

= 2 ≥ ∗




3-25

Figure 3.9 Solow Model with Saving

Dependent on Income Level

Δ = ()

There are twopossible steady

states in thiseconomy; a countrygravitates towardone or the otherdepending on itsinitial level of capital




The effect of income on saving

A country at the lower steady state is «trapped»there: its level of income per capita is low because itssaving rate is low, and its saving rate is low becauseits income per capita is low (multiple steady states: acountry’s initial position determines which SS)

In the case in which saving is endogenous, a countrywith income below its steady state will also have alow saving rate, and this low saving rate will reducethe rate of growth

li d h




Government policy and thesaving rate

Solow model: countries with higher saving ratesshould have higher levels of income per capita

Government that raise the saving rate can thus be atool to raise the level of national income

Government can raise savings by using its budget

Budget deficits (negative saving) reduce the nationalsaving rate and reduce investment and growth

Governments can influence the private saving rates

setting up national old-age pension plans

Th i d f ll f i l




The rise and fall of capitalrevisited

The belief that the accumulation of capital is the keyto economic growth reached its high after WWII

Economists’ view on capital’s role in producing growthin turn influenced the policies that developingcountries and international agencies followed in

attempting to promote economic development These policies are now viewed as having failed.

Injections of capital failed to produce significantgrowth in developing countries

In recent decades, more attention to factors such aseducation, technological change, and institutions

research methods in macro

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