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INVESTMENT
Macroeconomics II
INV
ES
TM
EN
T
Class 5
A Road Map
1. Introduction
2. The Accelerator Hypothesis of Investment
2.1 The Accelerator Model
2.2 Assessing the Simple Accelerator
3. The Neoclassical Theory of Investment
3.1 The User Cost of Capital
3.2 The Desired Capital Stock
3.3 From the Desired Capital Stock to Investment
4. Tobin’s q Theory
4.1 Investment and the Stock Market
4.2 Investment and Expectations of Profit
5. Investment in Inventories and Housing
INV
ES
TM
EN
T
Class 5
Motivation
Unemployment and investment in EU28
1.
Intr
oduct
ion
Introduction 1/10
Net capital stock per person employed (2005 prices thous. EUR)
0
50
100
150
200
250
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Germany France Latvia Lithuania
Poland United Kingdom United States Japan
1.
Intr
oduct
ion
Introduction 2/10
Gross capital formation and Gross fixed capital formation (% of GDP,
average 2000-2010)
0
5
10
15
20
25
30
35
40
45
China Germany India Japan Korea,
Rep.
Poland UK USA Brazil
GCF GFCF
1.
Intr
oduct
ion
Introduction 3/10
Consumption, investment and GDP in EU27 (2000=100)
1.
Intr
oduct
ion
Introduction 4/10
China: GCF, GFCF, and GDP growth rates
0
5
10
15
20
25
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
gcf gfcf gdp
1.
Intr
oduct
ion
Introduction 5/10
India: GCF, GFCF, and GDP growth rates
-10
-5
0
5
10
15
20
25
30
35
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
gcf gfcf gdp
1.
Intr
oduct
ion
Introduction 6/10
Germany: GCF, GFCF, and GDP growth rates
-20
-15
-10
-5
0
5
10
15
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
gcf gfcf gdp
1.
Intr
oduct
ion
Introduction 7/10
Japan: GCF, GFCF, and GDP growth rates
-20
-15
-10
-5
0
5
10
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
gcf gfcf gdp
1.
Intr
oduct
ion
Introduction 8/10
USA: GCF, GFCF, and GDP growth rates
-25
-20
-15
-10
-5
0
5
10
15
20
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
gcf gfcf gdp
1.
Intr
oduct
ion
Introduction 9/10
Poland: GCF, GFCF, and GDP growth rates
-20
-15
-10
-5
0
5
10
15
20
25
30
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
gcf gfcf gdp
1.
Intr
oduct
ion
Introduction 10/10
CONCLUSIONS:
Large differences in capital intensity persist
Fixed investment is the major component of
investment spending
Investment is much more volatile than consumption
and moves procyclically
Inventory change exhibits much more sharp swings
than fixed investment (it is a procyclical, usually
leading indicator)
2. T
he
Acc
eler
ator
Hypoth
esis
of
Inves
tmen
t
2.1 The Accelerator Model 1/2
The accelerator hypothesis of investment relies on a
simple idea that firms attempt to maintain a fixed ratio
of their stock of capital to their expected sales:
e
tt YK
Net investment* is equal to the difference between the desired capital stock and the stock of capital inherited from the preceding period:
1
tt
N
t KKI
*Definition K
t-1 = capital stock at the end of period t-1; d = depreciation rate
111; tttttt
N
t dKKKIKKI
2. T
he
Acc
eler
ator
Hypoth
esis
of
Inves
tmen
t
2.1 The Accelerator Model 2/2
Estimating expected sales
We assume adaptive method of estimating sales expectations which we encountered in the formation of expectations of permanent income
The level of investment depends on the change in expected output
Assume that firms always manage to acquire new capital quickly enough to keep their actual capital stock equal to its desired capital stock in each period. Then
e
tt
e
t
e
t YYjYY 111
1
11
have we1for
t
N
t
e
t
e
t
e
ttt
N
t
YIj
YYYKKI
2. T
he
Acc
eler
ator
Hypoth
esis
of
Inves
tmen
t
2.2 Assessing the Simple Accelerator 1/3
NMS: New Member States; OMS: Old Member States; FCC
(former cohesion states): Spain, Ireland, Portgal.
2. T
he
Acc
eler
ator
Hypoth
esis
of
Inves
tmen
t
2.2 Assessing the Simple Accelerator 2/3
NMS: New Member States; OMS: Old Member States; FCC
(former cohesion states): Spain, Ireland, Portgal)
2. T
he
Acc
eler
ator
Hypoth
esis
of
Inves
tmen
t
2.2 Assessing the Simple Accelerator 3/3
Conclusion:
Net investment does not respond instantaneously to changes
in output growth, but rather displays noticeable lags
The lag is not of uniform length, nor does net investment
respond to changes in real GDP growth with uniform speed
Making the accelerator model more realistic:
In addition to the direct cost of investment, there are
adjustment costs which lead to lags in the adjustment of the
actual capital stock to the level of the desired capital stock.
Flexible accelerator model:
1
1 10
t
e
t
N
t
tt
N
t
KYI
KKI
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.1 The User Cost of Capital 1/5
Even the flexible accelerator theory of investment
assumes that the desired capital stock is a fixed
multiple of output.
This specification ignores the fact that different levels
of output can be produced with the same level of capital
and varying the labor input
The optimal choice of a capital-labor mix to produce a
given output depends on the ratio of the two factor
costs
The user cost of capital uc is the cost to the firm of
employing an additional unit of capital for one period
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.1 The User Cost of Capital 2/5
The user cost of capital depends on several factors
The interest rate represents the cost of borrowing or
the opportunity cost of the investment project
The depreciation rate indicates the per period decline
in value of the capital good due to physical
deterioration and obsolescence
The interest and depreciation cost are adjusted by
price changes for capital goods. Rapid price increases
mean that used capital goods can sometimes be resold
for more than their cost when new
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.1 The User Cost of Capital 3/5
The standard expression for the user cost of an asset in nominal terms is
where PK is market value of an asset at current prices
)(
gain capitalpreciation
-de ofcost paymentinterest
nominal
K
KK
P
PdiPuc
If we assume that the expected capital gain is equal to expected inflation, the user cost converted to real terms becomes
where pK is market value of an asset at constant prices and r is the real interest rate
)(
preciation -de ofcost
paymentinterest
drpuc K
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.1 The User Cost of Capital 4/5
Changes in the user cost of capital (in %) i G7 countries.
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.1 The User Cost of Capital 5/5
Fiscal policy can have a major effect on investment by altering the user cost:
Imposing a tax on a firm’s income effectively adds another element to user cost
Firms can cut their corporate income tax by deducting the value of depreciation of plants and equipment
= corporate tax rate
z = present value of depreciation allowances (per 1 unit invested)
1
1)(
zdrpuc K
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.2 The Desired Capital Stock 1/4
Jorgenson’s theory assumes that a business firm is
willing to undertake an investment project when it
expects that a profit can be made.
An extra unit of capital will not be purchased unless
the expected marginal product of capital (MPK f ) is
at least equal to the real user cost of capital
ucMPK f
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.2 The Desired Capital Stock 2/4
The determination of the desired capital stock
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.2 The Desired Capital Stock 3/4
Changes in the desired capital stock: A decline in the
real interest rate raises the desired capital stock
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.2 The Desired Capital Stock 4/4
Changes in the desired capital stock: An increase in the
expected future MPK raises the desired capital stock
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.3 From the Desired Capital Stock
to Investment
The desired capital stock is a multiple of expected
output
The desired capital/output ratio depends on the user
cost of capital
Net investment depends on income, and the variables
which represent elements of the user cost of capital
e
tt YK
uc
1,,,, t
f
t
e
t
N
t KMPKdrYII
3. T
he
Neo
clas
sica
l
Theo
ry o
f In
ves
tmen
t
3.3 From the Desired Capital Stock
to Investment
The drivers of investment in advanced OECD
countries
Long run elasticity of capital stock with respect to:
Period 1985-2013 1993-2013
Output 1,23 1,05
Interest rate -0,08 -0,02 (not
significant)
Product market
regulation index
-0,06 -0,09
4. T
obin
’s q
Theo
ry
4.1 Investment and the Stock Market 1/3
Tobin’s q theory, instead of positing a desired level of
capital and a separate process of adjustment, merges
adjustment costs directly into the firm’s single
calculation of the desired rate of investment at each
moment of time
Tobin’s theory develops an idea that the attractiveness
of purchasing new capital depends on the market value
of capital in the stock market as compared with the cost
of purchasing the capital
4. T
obin
’s q
Theo
ry
4.1 Investment and the Stock Market 2/3
A quantitative measure that reflects changes in market value relative to the cost of purchasing the capital
Investment is an increasing function of q ratio
where a denotes a constant
I/K=d if q=1
I/K>d if q>1
stock capital theof valuethe
valuemarket stock sfirm' theq
dqaK
I 1
4. T
obin
’s q
Theo
ry
4.1 Investment and the Stock Market 3/3
Investment and Tobin’s q in the USA 1960Q1:2009Q2
4. T
obin
’s q
Theo
ry
4.2 Investment and Expectations of
Profit 1/2
The firm’s stock market value reflects the net
present value of its discounted expected profits:
If people have static expectations (expect the future
to be like the present) then
)1)(1(
)1(
1 1
21
e
tt
e
t
t
e
te
trr
d
rV
dr
Vt
te
t
4. T
obin
’s q
Theo
ry
4.2 Investment and Expectations of
Profit 2/2
Conclusions:
Tobin’s q depends positively on the expected present
value of future profits per unit of capital
The higher current or expected profits, the higher the
expected present value and the higher the level of
investment
The higher current or expected real interest rate, the
lower the expected present value and thus the lower the
level of investment
5.
Inves
tmen
t in
Ho
usi
ng
Housing investment
The concepts of the user cost of capital and future
marginal product and accelerator principle apply
equally well to inventory investment
The firm may want to keep an inventory of a multiple
of one month’s sales. The attractive aspect of using an
accelerator-type of theory to explain inventory
investment is that there are sizable swings in
inventories that follow business fluctuations
Inventory investment responds to interest rates.
5.
Inves
tmen
t in
Ho
usi
ng
Housing investment
Equilibrium in the housing market (Mankiw)
5.
Inves
tmen
t in
Ho
usi
ng
Housing investment
House prices and macroeconomic fundamentals (BIS, WP236)
