Intermediate Macroeconomics
Lecture 11 - Investment
Zsófia L. Bárány
Sciences Po
2014 April
Roadmap
I
investment in the data
I
investment decisions in a two period model
I
investment and asymmetric information: financial crisis
Three types of investment
1. business fixed investment:
businesses’ spending on equipment and structures for use in
production
2. inventory investment:
the value of the change in inventories of finished goods,
materials and supplies
3. residential investment:
purchases of new housing units
Investment in the US data
Understanding private fixed investment
I
let us focus on firms
I
if firms are forward looking then investment decisions depend
on expectations about the future
the decision to buy a machine depends on:
I
I
I
I
the cost of buying it today
the present discounted value of the additional expected future
profits from having this machine
what determines the additional expected future profit of
buying a machine?
0
I
I
future marginal product of capital (MPK 0 = ∂Y
∂K 0 ):
if there is an improvement in future technology, z 0 , then the
marginal product of future capital, MPK 0 , will be higher and
profits will be larger
taxes:
corporate income tax and investment tax credits
Investment decisions in a two-period model
I
I
focus on representative firm
present value of profits depends on:
I
technology
I
choices of current and future employment
choice of future capital (or current investment), given initial
level of capital
I
Investment decisions in a two-period model
I
I
focus on representative firm
present value of profits depends on:
I
I
I
technology
current output Y = zF (K , N), future output Y 0 = z 0 F (K 0 , N 0 )
choices of current and future employment
choice of future capital (or current investment), given initial
level of capital
future capital stock: K 0 = (1 − d)K + I
Investment decisions in a two-period model
I
I
focus on representative firm
present value of profits depends on:
I
I
I
technology
current output Y = zF (K , N), future output Y 0 = z 0 F (K 0 , N 0 )
choices of current and future employment
choice of future capital (or current investment), given initial
level of capital
future capital stock: K 0 = (1 − d)K + I
I
current profits π = Y − wN − I
I
future profits π 0 = Y 0 − w 0 N 0 + (1 − d)K 0
I
present value of profits V = π +
π0
1+r
Optimal choices
I
employment is a flow variable and can be chosen every period
I
↔ future capital depends on current investment
intuitively: equate marginal benefit to marginal cost
I
I
I
I
current labor demand (N d ): MPN = w
0
future labor demand (N d ): MPN 0 = w 0
current investment (I ):
MB(I ) = MC (I )
MPK 0 +1−d
1+r
I
marginal benefit of investment is MB(I ) =
I
marginal cost of investment is MC (I ) = 1 since one unit of
output costs 1 (numeraire) and can be used for investment
I
⇒ optimal investment is such that
MPK 0 + 1 − d
= 1 ⇒ MPK 0 − d = r
1+r
can also write as
0
MPK
| {z }
additional output
=
d
+ r}
| {z
user cost of capital
Optimal choices
I
mathematically:
I
I
choosing I is equivalent to choosing K 0 as I = K 0 − (1 − d)K
– from the capital accumulation equation
0
π0
⇒ given K , choose N d , N d , K 0 to max V = π + 1+r
plugging in for π, π 0 , I we get
V = Y − wN − (K 0 − (1 − d)K ) +
I
Y 0 − w 0 N 0 + (1 − d)K 0
1+r
First order conditions:
I
(N d ):
0
I
I
(N d ):
∂Y
∂N
− w = 0 ⇒ MPN = w
∂Y 0
∂N 0
−w 0
1+r
(K 0 ): −1 +
= 0 ⇒ MPN 0 = w 0
∂Y 0
∂K 0
+1−d
1+r
= 0 ⇒ MPK 0 − d = r
Optimal choices
Note: MPK 0 − d = r pins down the optimal K 0 , which implies
I = K 0 − (1 − d)K . It is possible that I < 0.
Shifters of labor demand
Example:
* increase in current TFP
→ higher z ⇒ higher MPN
* increase in the current
capital stock
→ higher K ⇒ higher MPN
Shifters of investment demand
Example:
* increase in expected future
TFP
→ higher z 0 ⇒ higher MPK 0
* decrease in the current
capital stock
→ lower K ⇒ no change in
MPK 0 , requires higher I to
reach the same K 0
Current vs expected future profit
I
I
the model we went through suggests that investment
decisions depend on expected future profits
however, empirical findings show that investment moves with
fluctuations in current profits as well
I
I
some firms with highly profitable investment projects but low
current profits appear to invest too little
current profits appear to affect investment even after
controlling for the expected present value of profits
Current vs expected future profit
I
I
the model we went through suggests that investment
decisions depend on expected future profits
however, empirical findings show that investment moves with
fluctuations in current profits as well
I
I
I
suppose a firm wants to invest (because expected future
profits are high), but current profits are low
I
I
I
some firms with highly profitable investment projects but low
current profits appear to invest too little
current profits appear to affect investment even after
controlling for the expected present value of profits
the firm must finance the investment through loans, or by
issuing bonds or shares
if the firm faces financing constraints, then its optimal
investment might not be feasible
⇒ borrowing constraints might affect investment
– similar to the effect of borrowing constraints on consumption
Investment with asymmetric information
I
suppose there are many firms in the economy – some good,
some bad
I
I
I
I
I
I
bad firms: borrow in the credit market, consume the proceeds
as executive compensation, then default
good firms: borrow, use it for investment, and repay
asymmetric information: lenders cannot distinguish good from
bad firms
⇒ higher loan rate (borrowing rate) than deposit rate, rb > r
includes a default premium to compensate for borrowers who
default
interest rate spread x = rb − r reflects the severity of the
asymmetric information problem
optimal future capital stock for firms that borrow:
MPK 0 − d = rb ⇒ MPK 0 − d − x = r
I
the interest rate spread x acts to reduce the net marginal
product of capital given r
Investment with asymmetric information
I
when the asymmetric
information problem
worsens, the interest rate
spread x increases
I
⇒ investment demand
shifts left, and the firm
chooses to invest less for
any r
I
the theory predicts a
negative relationship
between investment and
the default premium
Data: investment and the interest rate spread in the US
measure of interest rate spread: the difference between the interest
rates on AAA-rated and BAA-rated corporate bonds
Note: in recessions (1974-75, 1981-82, 1990-91, 2001,2008-10)
spread soars, investment plummets
Summary
our model suggests
I
desired future capital level depends on expected future profits
→ investment depends on π 0 and current capital
I
current profits should not matter
in the data
I
some firms with high expected future profit do not invest
enough
I
and current profits impact current investment
I
→ suggests the presence of borrowing constraints
I
in the presence of asymmetric information the interest rate
spread has a negative impact on investment
→ confirmed in the data