Download - Revised Investment
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InvestmentAnthony Murphy
Nuffield [email protected]
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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 importantelement offiscal policy.
On the supply side, long run growth is related tothe size of the capital stock, which is justcumulated investment.
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Classifications of Investment Etc.
Gross fixed capital formation plus changes ininventories.
Gross investmentdepreciation = net investment
Business investment plus residential investmentplus inventories
What about R&D, software and other intangibles? Private v. public investment e.g. infrastructure.
Should schooling count as investment?
1t t tK I K
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Neo-Classical Investment Model
la Jorgenson (e.g. 1979) Risk neutral firm (Fisher separation & Modigliani-
Miller theorems) maximises present value ofprofits.
Price taker if competitive firm.
Set out equations and derive demand for flow ofinvestment from demand for desired capital
stock. FOCs:MPL = w (real wage) &MPK= c = pI.(r
+ -pI/pI) (real rental / cost of capital).
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The Real Rental / Cost of Capital
Real rental / cost of capital c = pI.(r + -pI/pI) is
the appropriate price of a capital good.
pI= real price of capital good; r= real interest rate;
= depreciation rate;
pI/pI= rate of appreciation of capital goodsrelative to output prices; assume approx zero.
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Some Comparative Statics
Can look at effects of changes in:
Technology gains;
Real interest rates;
Tax incentives.
Cobb-Douglas example: Y = ALK1-exp(t) andMPK=(1-)Y/K.
K*= (1-)Y/c.
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Marginal productivity
of capital
Output
c=slope
MPK
cK
K
K
Marginal cost of capitalC
Y=F K( )
K
K
Fig. 6.13
Output
Capital stock
Capital stock
Optimal
capital stock
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Technological
progress makes
more output
possible with thesame capital
stock. Desired
capital stock
increases.
Marginal productivity
of capital
Output
cK
c=slope
K
K
MPK
New
C
Old
MPK
K
K
Fig. 6.14
Output
Capital stock
Capital stock
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Problems with Baseline Model
Instantaneous speed of adjustment of capitalstock unrealistic.
No role for future expectations (apart fromappreciation term pI/pI).
Note: The so called accelerator model,It=Kt+ Kt-1= Ytholds when ctis approx. constant
(i.e. when rtandpItare approx. constant) in thelong run or when credit constraints bind.
Called accelerator model cos estimated between2 and 3.
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Adding Dynamics
Add ad hoc dynamics e.g. simple partialadjustment model:
Add quadratic adjustment costs and rationalexpectations ( la Sargent).
Now expectations of all future prices etc.
matter. No free lunch! Need to model expectations.
Hard to model realistically.
*
1 1( )
t t t t t K I K K K
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Tobins q, the Stock Market and
Investment Share prices can be thought of as markets best
estimate of value of present and future profits, sothey capture future expectations.
Aside: Stock markets are forward looking. Whatabout irrational exuberance of dot-combubbles etc.?
Tobin (1969) suggested that the rate of investmentis related to q = market value of installed capital/ replacement cost of installed capital, with q =1 in equilibrium.
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The q-theory of investment
Tobins q
InvestmentI/K
01
Fig. 6.15
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The Appeal of Tobins q
Simple model - (I/K)tis increasing in qt. Intuitively appealing but no formal model.
Relationship to previous models? Negativeinterest rate effects work thru stock market
valuation. Ditto effects of technology gains andtax changes.
In addition, q should take account of uncertainty,growth in future demand, announcement effects
etc. Tobins q is like a sufficient statistic - given q,
other information (both observed and unobserved)does not matter.
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Micro Foundations of Tobins q
Can derive a Tobins q type model of investmentin an inter-temporal setting with costs ofinstalling investment e.g.
Installation costs explain why q is not alwaysequal to one. These additional costs slow theadjustment to the long run.
Diagram ofMCIandMPK.. However, in this set up, investment depends on
marginal q, as opposed to the average q proposedby Tobin.
2 212
1
( / )t t t t t
K I I K K
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Micro Foundations of
Tobins q (Contd) Hayashi (1982) et. al. showed that marginal q
equals average q when:
- The firm is a price taker;- The production function displays constantreturns 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 correctlyvalues future profits.
Fi 6 17
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Tobins q=1 in a world of no adjustment costs
(a)
Presentval
ueofMPK,
costof
capital
1
I K( )
MPK1
MPK=Marginal return of new investment
C
If there were no costs of
adjustment, the present value
of the marginal cost of capital
would be independent of theinvestment rate.
Note if there were nodepreciation, the investment
rate, I/K, = K/K, the rate of
change of the capital stock.
Fig. 6.17
Investment rate (I/K)
Fi 6 17
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Tobins qwhen adjustment costs are significant
(a)
Presentval
ueofMPK,
costof
capital
1
I K( )I K( )
1q
Marginal cost
of investment
MPK1
C
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.
Fig. 6.17
Investment rate (I/K)
MPK=Marginal return of new investment
A
Fi 6 17
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Tobins q
(b)
Presentval
ueofMPK,
costof
capital
A
1
1I K( )
1q
Marginal cost
of investment
MPK1MPK2
2I K( )
2q B
With the investment ratecorresponding to the rate
at point A, in the following
period there will be more
capital and a lowerMPK.
The investment rate next
period will fall too (as will
Tobins q), ultimately
heading toward a value ofunity and no more
investment.
Fig. 6.17
Investment rate (I/K)
MPK=Marginal return of new investment
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Tobins q In Practise
Hayashi (1982) estimated a simple investmentequation 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 qtis about 5.
Problematic equation. Why?
Adding some dynamics helps a bit.
However, other quantity type variables matter (soq is not really akin to a sufficient statistic).
Lower correlation between (I/K)tand qtin recentyears.
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Empirics (Contd)
There are a large no. ofmicro (panel data) andmacro (time series) studies of the q theory ofinvestment.
Macro studies frequently find:
- Price effects: a modest role for capital costs (qand/or its components including the real interestrate);
- Quantity effects: a substantial role for output
or cash flow variables (since, in the UK and US, alot of investment is financed from retainedearnings).
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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 thefirm level;
The sensitivity of investment to cash flow andprofits, which may imply a high incidence ofcredit constraints;
The consistency of observed high hurdle ratesfor investment with the option value of waiting;
The determinants of international investment e.g.FDI.
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Overview of Investment
Investment is the most volatile component ofaggregate demand.
The demand for capital depends on real interestrates, current and expected future output andtaxes.
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.