Macroeconomics
Chamberlin and Yueh
Chapter 3
Lecture slides
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Investment
•
•
•
•
•
•
Theories of Fixed Business Investment
Optimal Capital Stock Model
Tobin’s q
Inventory Investment
Residential Investment
Credit Rationing and Investment
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
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Learning Objectives
• Defining investment and its three main components
• Using the optimal capital stock model to explain changes in business
investment
• Constructing Tobin’s q as a forward-looking model of business
investment
• Identifying the factors that are responsible for inventory investment
• Understanding the main determinants of residential investment
• Explaining how the supply of investment finance can determine
aggregate investment
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What is investment?
• Private investment represents additions to the
nation’s capital stock. Investment is important
because it plays a dual role in the economy.
• First, it is part of aggregate demand, so it enters
the circular flow of income and determines output
movements in the short run.
• Second, by augmenting the nation’s stock of
productive assets, investment is central to the
determination of long run economic growth.
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The Importance of Investment
• Although investment expenditures constitute a much smaller part of
aggregate demand than consumption, the pace and pattern of business
investment is central to the understanding of economic activity.
• Investment is much more volatile than both consumption and GDP.
• Also, investment is often seen to be a leading indicator of GDP,
meaning that changes in investment predict future movements in output.
• Empirical evidence leads us to believe that investment may be an
important factor in accounting for business cycles.
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GDP, Investment, Consumption for
the UK
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Components of Private Investment
• The three main components of private
investment:
• fixed business investment,
• residential investment, and
• changes in the stock of inventories.
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Components of Investment, UK
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Theories of Fixed Business
Investment
• There are two major models of note, which share very
similar foundations.
• The optimal capital stock model argues that firms have a
desired level of capital stock and investment simply acts to
move the current capital stock in that direction.
• The second is known as the q theory of investment (or
Tobin’s q). When investment is undertaken, most returns are
accrued in the future; therefore, the decision to invest must
be forward-looking. As stock markets value firms according
to their expected future cash flows, an important feature of
q theory is the linking of investment decisions to stock
market prices.
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Optimal Capital Stock Model
• Also referred to as the Neoclassical model
of investment.
• The model argues that firms will settle on an
optimal level of capital stock, which is
where profits are maximised.
• Investment is then determined implicitly; it
is the required additions or reductions to the
capital stock that move it from its current to
its optimal level.
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Optimal Capital Stock Model
• Profit maximisation is the key to the
investment decision. Firm profits are
calculated in the conventional way: as total
revenue minus total costs.
  TR  TC
• Total revenue is found by multiplying the
output of the firm (Y) by the price at which
it is sold (P):
TR  PY
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Optimal Capital Stock Model
• The relationship between a firm’s output and
its inputs of capital is described by a
production function:
Y  F K 
• A common assumption is that the production
function experiences diminishing returns to
capital.
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Firm Production Function
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Marginal Product of Capital
• The marginal product of capital (MPK) tells us how total
output changes when the capital stock changes by one unit:
Y
MPK 
K
• As the production function displays diminishing returns to
capital, it must be the case that the marginal product of
capital (MPK) falls as the installed capital stock rises.
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MPK function
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Marginal Revenue Product of Capital
• Given that total revenue will be given by, the
change in total revenue following a change
in capital stock will be given by the
marginal revenue product of capital
(MRPK). The MRPK can be thought of as
the value of an extra unit of capital.
MRPK  P  MPK
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Costs
• The cost of purchasing K units of capital is
given by PKK. This is made up of the price
of a unit of capital, PK, and the total units
installed, K.
• However, the firm does not buy the capital
itself, but rents it from capital leasing firms
at the rental rate of r. This rental rate can
simply be thought of as the interest rate.
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Costs
• Therefore, the total cost of installing K units
of capital is:
TC  rPK K
• The marginal cost of capital is the cost of
installing one extra unit of capital stock:
MC  rPK
• This cost is constant and does not change
with the amount of capital stock already
installed.
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Profit Maximisation
• Given the costs and revenues involved in
installing capital, the firm can work out the
size of the capital stock that would maximise
its profits:
  PFK   rPK K
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Profit Maximisation
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Profit Maximisation
• Profits will be maximised at the level of
capital stock where the marginal revenue
product of capital is equal to the marginal
cost, or the optimal level of capital stock:
P.MPK  rPK
• It is only at the optimal level of capital stock
where there is no incentive for the firm
invest or disinvest.
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Firm Investment
• Having established the optimal capital stock,
this model predicts that firm investment will
be given by a simple relationship:

I K K
• Investment is determined implicitly by the
firm seeking to move their capital stock
towards its optimal level.
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What factors affect investment?
• If all firms were at their optimal (profit
maximising) level of capital stock, then what
factors would lead to a change in
investment?
• This simple model argues that anything
which leads to a change in the level of the
optimal capital stock will induce investment.
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Productivity Shocks
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Price of output
• Changes in the price of output would have a similar effect
as changes in productivity.
• The total revenue curve would again shift upwards and the
marginal revenue product of capital schedule will shift
outwards. The consequence will once again be that the
optimal capital stock will be higher, thereby encouraging
firm investment.
• This might account for some of the pro-cyclical nature of
investment. When the economy is performing well,
aggregate demand may be strong which supports higher
prices and encourages investment. Likewise, in a recession,
low demand could lead to poor sales and discounted prices,
discouraging investment.
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Price of capital goods
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Role of government policy
• The cost of capital can be adjusted to reflect the
presence of taxes and subsidies:
PK  1   PK
• A tax on capital implies that   0 . Consequently,
the optimal capital stock and investment will both
fall following an increase in these taxes.
• However, a subsidy,   0 , would have the opposite
effect and could be used to encourage investment.
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Interest rate changes
• Interest rates will affect capital in entirely
the same way as the changes in the prices of
capital goods.
• The interest rate is seen as the opportunity
cost of capital, instead of investing in capital
goods there is always the possibility of
saving in the bank.
• Therefore, changes in the interest rate will
imply changes in the rental rate of capital.
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Criticisms of the Optimal Capital
Stock Model
• The model is not forward-looking, so it does
not allow any room for investment to be
determined by expectations.
• Second, the capital stock is assumed to
always change instantaneously to its new
optimal level.
• These were incorporated into the theory,
Tobin’s q.
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Tobin’s q
• In its most simplest of guises, Tobin’s q can be
written as follows: q = Market Value of Firm /
Replacement Cost of Installed Capital.
• The market value of a firm is determined by the
expected discounted future cash flows that it will
generate. The replacement cost of installed capital
is simply the price of purchasing that firm’s capital
stock. Tobin’s q is just the ratio of the two.
• Therefore, changes in q will lead to changes in
investment.
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Tobin’s q
• If q>1, then every £1 of installed capital would create more
than £1 in market value. Installed capital is more valuable
than uninstalled capital so investment would be positive.
• When q=1, every £1 of installed capital will create an
additional £1 of market value. In this case, installed and
uninstalled capital has the same value and investment would
be zero.
• Finally, if q<1, then uninstalled capital is more valuable
than installed capital. Investment would be negative; a firm
would be able to achieve more by selling its physical capital
than it would lose in market value.
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Tobin’s q
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Stock Markets and Investment
• If it is the stock market that represents the
value of a firm, then it is not surprising to
expect a linkage between the stock market
and investment. Changes in the value of
stock markets should be positively correlated
with future changes in investment.
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UK Stock Market and Investment
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Evidence of Tobin’s q
• There does appear to be some correlation between
movements in the stock market and investment. However,
the evidence supporting this relationship is by no means
clear cut. This may be for a number of reasons.
• First, not all firms are quoted on the stock market. A
significant amount of investment is undertaken by these
firms, so this would dilute any potential relationship
between stock prices and investment.
• Second, stock market valuations may be determined by
factors other than fundamentals related to a firm’s future
cash flows. It is widely recognised that stock markets tend
to be fairly volatile.
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Tobin’s q and the Market Value of
the Firm
• The market value of the firm is given by the
sum of its expected discounted future cash
flows. The revenue the firm generates in
each period is given as before:
P.F K t 
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Tobin’s q and the Market Value of
the Firm
• The value of the firm at the present time is
given by the present discounted value of all
future revenues:
P.F K1  P.F K 2  P.F K 3 
V0 


 ............
2
3
1  r  1  r 
1  r 
• The cost of the initially installed capital
stockK 0  is also as before:
P K
K
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0
Rewriting Tobin’s q
• Tobin’s q =
V0
q
PK K 0
• Further simplifying, if we continue to
assume that capital depreciation is zero, then
the capital stock will be durable and the
same in all periods, so:
V0 
P.F K  1  r  P  F K 


1  r 
r
r
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Rewriting Tobin’s q
• Tobin’s q
P.F K 

rPK K
• The same factors that cause a change in investment in the
optimal capital stock model are likely to cause a change in
investment in the q-based model. Investment is likely to
rise if productivity or output prices rise, or the interest rate
falls – these factors will lead to an increase in the market
value of the firm. A fall in the cost of capital goods would
also encourage investment.
• The main feature added by q-based models is that current
investment will also be influenced by the future values of
these variables.
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Adjustment Costs
• What factors might account for the speed at which this
investment takes place?
• The analysis so far has assumed that the marginal cost of
changing the capital stock is simply given by the price of a
unit of physical capital. The firm may also face costs in
installing or uninstalling capital, which increase with the
size of the investment. It is much more expensive to make
large wholesale changes to the capital stock then just small
fine-tuning changes.
• Installation costs will increase with the rate of investment.
Also, installation costs are transitory; once the capital is
installed no further costs are levied.
• The presence of these installation or adjustment costs
suggests that it would be optimal to make small changes to
the capital stock.
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Tobin’s q
• Adding this insight to the q-theory enables
us to write down a rule that determines
investment:
1
I 

q  1
• Investment will increase when q>1 and fall
when q<1. The parameter  reflects
installation costs. As these rise, investment
will respond more gradually.
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Inventory Investment
• There are several reasons why firms may hold inventories.
• Holding stocks of inventories would allow firms to smooth
production. Changes in inventories act as a shock absorber
to fluctuations in demand. Production smoothing would be
the most efficient way of organising production. Production
smoothing would act to minimise these costs.
• Secondly, holding inventories would enable the firm to
avoid stock outs. This is where the firm has to turn away
customers because it has no stock to sell. Clearly, stock
outs would be poor for revenue.
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Production Smoothing and the
Pro-cyclicality of Inventory Investment
• The main rationale for smoothing production is to reduce
average total cost over time/the economic cycle.
• A firm’s total cost function is assumed to be convex.
Convexity implies that the marginal cost of an extra unit of
output increases with the level of output.
• The convexity of the total costs curve is sufficient reason to
use inventories to smooth production.
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Total cost function
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Production smoothing
• The benefits of production smoothing are directly related to
the convexity of the total cost curve. The more convex, the
larger the gains from production smoothing.
• Instead, if the total cost function was linear (so it is no
longer strictly convex), then the gains from production
smoothing would completely disappear. Linear total costs
imply constant marginal costs at all levels so there are no
gains to smoothing production.
• The cost gains from smoothing production need to be
weighed against the costs of storing inventories. As storage
costs become more significant, the pro-cyclicality of
inventory investment will increase. This is because the cost
gains from production smoothing are low because marginal
costs are fairly constant, or because storage costs are
relatively high so as to offset the cost savings from
smoothing production.
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Accelerator Model of Investment
• The accelerator model could apply to most types
of investment, but it is particularly relevant to
inventory investment.
• It states that inventory investment is likely to be
highly pro-cyclical.
• If firms hold stocks of inventories proportional to
output, then:
K  vY
inv
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Accelerator Model of Investment
• Changes in output would lead to
proportional changes in the stock of
inventories:
K inv  vY
• Therefore, inventory investment will
respond positively to changes in output:
I inv  vY
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Economic growth and inventory
investment in the UK
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Evidence
• Empirical evidence supports the accelerator model. A clear
positive correlation exists between economic growth and
inventory investment. The observed pro-cyclicality of
investment tends to reject the production smoothing model.
• It is argued that inventory investment fits the accelerator
model better than the other components of investment. The
reason for the stronger pro-cyclical movement of
inventories is most likely due to the fact that there are few
installation costs involved with adding to the stock of
inventories. Therefore, this investment will respond much
more spontaneously to changes in output than fixed
business investment.
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Residential Investment
• Residential investment refers to expenditure on
improving existing dwellings or building new ones.
The factors which determine residential investment
should conceivably share a common structure with
the q-theory explaining fixed business investment.
• Recall that according to the q-theory, a firm will
invest if expected discounted value of the cash
flows generated by that investment exceeds the
cost of the physical capital required.
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Residential Investment
• A house is an asset, so its value should reflect the
future discounted value of rents that it earns. Just
because a house might be owner-occupied does not
mean that this principle no longer applies.
• Strictly speaking, the owner is also the tenant, so
would in effect just be paying rent to himself which
would be a needless transaction. However, there is
still an implicit rental value involved.
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Residential Investment
• The current value of a house,V0H , should be
determined by the discounted value of the
future rentsR , R , R ,......... that it will earn:
1
H
0
V
2
3
R1
R2
R3



 ..............
2
3
1  r  1  r  1  r 
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Residential Investment
• If the rent is the same in all periods, then
H
0
V
R

r
• The physical cost of building a house is
given by the construction price, PH.
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Residential Investment
• Therefore, a q-theory for housing investment
would take the following form:
R
qH 
rPH
IH 
1
H
qH  1
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q theory of residential investment
• Where q theory fits residential investment well is
incorporating adjustment costs. Adding to the stock of
houses is a timely business, and therefore it is expected that
residential investment will respond slowly to changes in
house prices.
• Housing investment will respond positively to the rental
value of housing, and negatively with the interest rate and
the costs of construction. Also, the pace of investment is
likely to be influenced by installation costs connected to
building houses.
• The rental value of housing may be determined by several
factors. The most likely is of course income or
unemployment.
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Credit Rationing and Investment
• A significant proportion of investment is undertaken using
borrowed funds, this view implies that financial markets are
always prepared to lend sufficient funds to satisfy
investment demand.
• Once it is accepted that the supply of investment loans
might not be perfectly elastic, the supply side might become
an important determinant of aggregate investment.
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Imperfect Information
• Financial markets aim to intermediate between
savers and borrowers, but this role is beset with
problems of imperfect information.
• A firm borrowing to invest knows far more about
the risks and returns of the investment project than
the financial institution providing the finance. This
scenario where one party in a debt contract has
superior information to the other is known as
asymmetric information.
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Asymmetric Information
• Moral Hazard: When a debt contract between borrowers
and lenders allows for bankruptcy, it increases the incentive
of the borrower to undertake risky investments. If high risk
investments come to fruition, then they offer high returns to
the borrower; but, if they fail then the borrower can avoid
repayment by declaring bankruptcy.
• Adverse Selection: This explains why a lender may prefer to
ration credit rather than increase the interest rate. Riskaverse investors who undertake relatively safe but lower
return projects will be driven out of the loans market by an
increase in interest rate. Therefore, as the interest rate
increases, the lender is left with a higher proportion of
riskier investments in their loan portfolios.
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Effects on loans
• The first order effect of an increase in interest rates is to
increase the supply of loans. This is because every loan
made by a financial institution achieves a higher rate of
return so the credit supply curve is upward sloping.
• The second order effect though considers the impact of an
increase in interest rates on the quality of loans. Firstly,
moral hazard implies that as the interest rate increases the
marginal investment project undertaken becomes more
risky. In order to accept a loan at a higher interest rate, the
project undertaken needs to offer a higher rate of return and
therefore is likely to be riskier. Adverse selection implies
that as the interest rate continues to increase, those
undertaking safer but lower return investments will be
driven out of the market. Consequently, a point is reached
where interest rate increases reduce the expected returns
from loans due to deterioration in the quality of loans made.
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Supply of Loans
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Implications of asymmetric
information
• At low rates of interest the first order effect dominates, so
an increase in interest rates leads to an increase in the
supply of loans. However, there is a critical level of interest
rates where the second order effect begins to dominate and
further increases in interest rates reduce loan supply. This is
because at higher rates the quality of the loan portfolio
declines as it comes to be made up of increasingly risky
loans. As a result, the expected returns of the loan portfolio
will fall when the interest rate surpasses this critical level
and the loan supply curve becomes backward bending.
• Financial institutions would therefore be unwilling to
advance loans beyond the level. This shows how
asymmetric information produces the credit rationing result.
The availability of finance can be just as important as the
cost of finance as a determinant of investment.
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What factors affect the availability of credit?
• The supply constraint is determined by the critical level of
interest rate, where the credit supply schedule becomes
backward bending. Therefore, anything which alters the
shape of the supply curve is likely to have an effect on the
level at which credit rationing becomes relevant.
• There are strong grounds for arguing that the availability of
finance will be driven in large part by the same factors that
determine the demand for investment. Adverse changes in
the investment climate, due to any of the factors mentioned
previously in this chapter, will lead to a corresponding
adverse shift the risk and return structure of the investment
projects in the economy.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Adverse changes in investment
climate
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Firm profit levels and investment
• There is traditionally a link between firm profit levels and
investment.
• 1) High current profits might be an indicator of high future
profits and therefore encourage investment.
• 2) High profits breed strong optimism which makes
entrepreneurs more likely to undertake investment because
they are more confident about the stream of future cash
flows their business will generate.
• 3) Retained profits are a cheap source of investment funds
so enable investments to be made when otherwise the cost
of finance would be prohibitive. This is due to the fact that
internal funds will not be subject to the fees and service
charges, implicit profit margin, and repayment schedules
that would be imposed if borrowing at commercial rates
from financial institutions.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Theory of credit constraints
• The theory of credit constraints suggest two further reasons
why investment might be strongly related to profit levels.
• 1) If firms are able to sufficiently fund investment through
retained profits then the supply constraints from financial
markets become less binding.
• 2) Reduce the moral hazard problem that helps to create the
credit constraint in the first place. If a firm partially funds
an investment project through retained earnings it has a
greater stake in the project and more to lose if bankruptcy
results. Therefore, moral hazard is mitigated and financial
institutions would be more prepared to lend.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Global Applications 3.4
• Firm Level Surveys of Investment Intentions
• The Confederation of British Industry (CBI) conducts a
quarterly survey of manufacturing firms in the UK.
• There is a high positive correlation between investment and
optimism. As optimism refers to expectations over the next
four months, this provides evidence that investment
decisions are forward-looking with expectations about the
future being important.
• The survey reports that the availability of finance appears to
be a much more important factor than the cost of finance in
determining investment. This is particularly the case with
the ability to raise external finance which suggests that the
supply of investment funds and the issue of credit rationing
is also an important factor in determining investment.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• Investment plays a dual role in the economy. As part of
aggregate demand it can explain short run cycles in
economic growth, and by adding to the stock of productive
capital it might explain long run economic growth.
• Fixed business investment is the most significant part of
investment expenditures. The two main theories accounting
for this are the optimal capital stock and Tobin’s q models.
• The optimal capital stock model explains investment as the
change in the capital stock towards its profit maximisation
level. Investment will be positively related to the price of
output and productivity, and negatively related to interest
rates and the cost of capital goods.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• Tobin’s q implies that fixed business investment is driven
by expectations about the future. If expected future
discounted cash flows rise then investment will increase,
but due to adjustment costs investment will be spread over
time. Tobin’s q suggests that there is a direct link between
stock markets and investment.
• Inventories are stocks of inputs or semi-finished goods held
by firms. Inventory investment is a small part of total
investment, but important because it is highly pro-cyclical.
• The accelerator model suggests that investment is driven by
changes in output and that inventory investment is highly
pro-cyclical.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• Residential investment, particularly in new houses is a not
insignificant part of total investment. If property provides a
flow of rents, then it can be treated as an asset with its value
determined by the level of its expected future discounted
rental payments. For this reason, it is easy to adapt the
Tobin’s q model to explain this part of private investment.
• Finally, aggregate investment may be determined as much
the availability of investment finance as the demand for
investment. Due to problems of asymmetric information,
financial markets have imperfect information about the
quality of individual investment projects.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• Although an increase in interest rates implies that the
returns from lending finance increase, it might also have a
detrimental effect on the quality of loans.
• If the credit supply curve becomes backward bending then
investment finance might be rationed. If these constraints
are binding, then it opens up a new channel for investment
to be driven by internal finance such as retained profits.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning