Investment
Anthony Murphy
Nuffield College
anthony.murphy@nuffield.ox.ac.uk
Why Does Investment Matter?
• On the demand side, investment is very volatile.
• Investment spending is a primary link thru’ which
interest rates, and therefore monetary policy,
affect the economy.
• Tax policies affecting investment are an important
element of fiscal policy.
• On the supply side, long run growth is related to
the size of the capital stock, which is just
cumulated investment.
Classifications of Investment Etc.
• Gross fixed capital formation plus changes in
inventories.
• Gross investment – depreciation = net investment
Kt  I t   Kt 1
• Business investment plus residential investment
plus inventories
• What about R&D, software and other intangibles?
• Private v. public investment e.g. infrastructure.
• Should schooling count as investment?
Neo-Classical Investment Model
à la Jorgenson (e.g. 1979)
• Risk neutral firm (Fisher separation & ModiglianiMiller theorems) maximises present value of
profits.
• Price taker if competitive firm.
• Set out equations and derive demand for flow of
investment from demand for desired capital
stock.
• FOC’s: MPL = w (real wage) & MPK = c = pI.(r
+ δ - ΔpI/pI) (real rental / cost of capital).
The Real Rental / Cost of Capital
Real rental / cost of capital c = pI.(r + δ - ΔpI/pI) is
the appropriate price of a capital good.
• pI = real price of capital good;
• r = real interest rate;
• δ = depreciation rate;
• ΔpI/pI = rate of appreciation of capital goods
relative to output prices; assume approx zero.
Some Comparative Statics
Can look at effects of changes in:
• Technology gains;
• Real interest rates;
• Tax incentives.
Cobb-Douglas example:
• Y = ALαK1-αexp(γt) and MPK= (1-α)Y/K.
• K*= (1-α)Y/c.
Fig. 6.13
Y =F(K )
cK
OutputOutput
Optimal
capital stock
slope
=c
K
K
Capital stock
Marginal productivity
of capital
Marginal cost of capital
C
MPK
K
K
Capital stock
Fig. 6.14
New
cK
Output
Output
Old
slope
=c
K
K
Capital stock
Marginal productivity
of capital
C
MPK´
MPK
K
K
Capital stock
Technological
progress makes
more output
possible with the
same capital
stock. Desired
capital stock
increases.
Problems with Baseline Model
• Instantaneous speed of adjustment of capital
stock unrealistic.
• No role for future expectations (apart from
appreciation term ΔpI/pI).
• Note: The so called “accelerator model”, It = ΔKt
+ δKt-1= νΔYt holds when ct is approx. constant
(i.e. when rt and pIt are approx. constant) in the
long run or when credit constraints bind.
• Called accelerator model ‘cos estimated ν between
2 and 3.
Adding Dynamics
• Add ad hoc dynamics e.g. simple partial
adjustment model:
Kt  I t   Kt 1   ( Kt*  Kt 1 )
• Add quadratic adjustment costs and rational
expectations (à la Sargent).
• Now expectations of all future prices etc.
matter.
• No free lunch! Need to model expectations.
• Hard to model realistically.
Tobin’s q, the Stock Market and
Investment
• Share prices can be thought of as market’s best
estimate of value of present and future profits, so
they capture future expectations.
• Aside: Stock markets are forward looking. What
about “irrational exuberance” of dot-com
bubbles etc.?
• Tobin (1969) suggested that the rate of investment
is related to q = market value of installed capital
/ replacement cost of installed capital, with q = 1
in equilibrium.
Fig. 6.15
Investment I/K
The q-theory of investment
0
1
Tobin’s q
The Appeal of Tobin’s q
• Simple model - (I/K)t is increasing in qt.
• Intuitively appealing but no formal model.
• Relationship to previous models? Negative
interest rate effects work thru’ stock market
valuation. Ditto effects of technology gains and
tax changes.
• In addition, q should take account of uncertainty,
growth in future demand, announcement effects
etc.
• Tobin’s q is like a sufficient statistic - given q,
other information (both observed and unobserved)
does not matter.
Micro Foundations of Tobin’s q
• Can derive a Tobin’s q type model of investment
in an inter-temporal setting with costs of
installing investment e.g.
Kt  I t  1 2  2 ( I t2 / K t )   K t 1
• Installation costs explain why q is not always
equal to one. These additional costs slow the
adjustment to the long run.
• Diagram of MCI and MPK..
• However, in this set up, investment depends on
marginal q, as opposed to the average q proposed
by Tobin.
Micro Foundations of
Tobin’s q (Cont’d)
• Hayashi (1982) et. al. showed that marginal q
equals average q when:
- The firm is a price taker;
- The production function displays constant
returns to scale;
- Adjustment costs, per unit of I only depend on
the ratio of I/K.
• Otherwise, average q will not completely capture
expectations even if the stock market correctly
values future profits.
Fig. 6.17
Present value of MPK,
cost of capital
Tobin’s q=1 in a world of no adjustment costs
If there were no costs of
adjustment, the present value
of the marginal cost of capital
would be independent of the
investment rate.
C
1
MPK1
(I K )
Investment rate (I/K)
(a)
Note if there were no
depreciation, the investment
rate, I/K, = K/K, the rate of
change of the capital stock.
MPK=Marginal return of new investment
Fig. 6.17
Present value of MPK,
cost of capital
Tobin’s q when adjustment costs are significant
Marginal cost
of investment
q1
A
C
1
MPK1
(I K ) (I K )
However the faster we try to
install new capital, the more it
adds to the cost of that capital.
“Haste makes waste.” Hence
the upward slope of the
marginal cost of investment
with respect to the investment
rate.
Investment rate (I/K)
(a)
MPK=Marginal return of new investment
Fig. 6.17
With the investment rate
corresponding to the rate
at point A, in the following
period there will be more
capital and a lower MPK.
The investment rate next
period will fall too (as will
Tobin’s q), ultimately
heading toward a value of
unity and no more
investment.
Present value of MPK,
cost of capital
Tobin’s q
Marginal cost
of investment
q
1
q2
A
B
1
MPK2
(I K )2
MPK1
(I K )1
Investment rate (I/K)
(b)
MPK=Marginal return of new investment
Tobin’s q In Practise
• Hayashi (1982) estimated a simple investment
equation on US data for 1953 to 1976:
(I/K)t= const + 0.043qt
• R2 = 0.46, DW = 0.43 and the t stat on average qt
is about 5.
• Problematic equation. Why?
• Adding some dynamics helps a bit.
• However, other quantity type variables matter (so
q is not really akin to a sufficient statistic).
• Lower correlation between (I/K)t and qt in recent
years.
Empirics (Cont’d)
• There are a large no. of micro (panel data) and
macro (time series) studies of the q theory of
investment.
• Macro studies frequently find:
- Price effects: a modest role for capital costs (q
and/or its components including the real interest
rate);
- Quantity effects: a substantial role for output
or cash flow variables (since, in the UK and US, a
lot of investment is financed from retained
earnings).
Lots of Ongoing Research
• The effect of taxation on the cost of capital and q,
and hence investment (e.g. event studies);
• The “excessive” lumpiness of investment at the
firm level;
• The sensitivity of investment to cash flow and
profits, which may imply a high incidence of
credit constraints;
• The consistency of observed high hurdle rates
for investment with the option value of waiting;
• The determinants of international investment e.g.
FDI.
Overview of Investment
• Investment is the most volatile component of
aggregate demand.
• The demand for capital depends on real interest
rates, current and expected future output and
taxes.
• Investment reflects the adjustment of the existing
capital stock to the current demand for capital.
• Investment is a primary link from monetary policy
to aggregate demand.