Investment

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Investment

• Anthony Murphy
• Nuffield College
• anthony.murphy_at_nuffield.ox.ac.uk

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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
  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.

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Classifications of Investment Etc.

• Gross fixed capital formation plus changes in
  inventories.
• Gross investment depreciation net investment
• Business investment plus residential investment
  plus inventories
• What about RD, software and other intangibles?
• Private v. public investment e.g. infrastructure.
  
• Should schooling count as investment?

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Neo-Classical Investment Modelà la Jorgenson
(e.g. 1979)

• Risk neutral firm (Fisher separation
  Modigliani-Miller 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.
• FOCs MPL w (real wage) MPK c pI.(r d
  - ?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 d -
  ?pI/pI) is the appropriate price of a capital
  good.
• pI real price of capital good
• r real interest rate
• d depreciation rate
• ?pI/pI rate of appreciation of capital goods
  relative 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 ALaK1-aexp(?t) and MPK (1-a)Y/K.
• K (1-a)Y/c.

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Figure 6.13
Fig. 6.13
Output
Output
Optimalcapital stock
Capital stock
Marginal productivity of capital
Capital stock
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Figure 6.14
Fig. 6.14
cK
Output
Output
Old
Technological progress makes more output possible
with the same capital stock. Desired capital
stock increases.
Capital stock
Marginal productivity of capital
MPK
Capital stock
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Problems with Baseline Model

• Instantaneous speed of adjustment of capital
  stock unrealistic.
• No role for future expectations (apart from
  appreciation term ?pI/pI).
• Note The so called accelerator model, It ?Kt
  dKt-1 ??Yt 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 ? between
  2 and 3.

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Adding Dynamics

• Add ad hoc dynamics e.g. simple partial
  adjustment model
• 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.

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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,
  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.

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Figure 6.15
Fig. 6.15
The q-theory of investment
Investment I/K
Tobins q
0
1
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The Appeal of Tobins 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.
• 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 investment
  in an inter-temporal setting with costs of
  installing investment e.g.
• 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.

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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 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.

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Figure 6.17
Fig. 6.17
Tobins q1 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.
Present value of MPK,cost of capital
Note if there were no depreciation, the
investment rate, I/K, DK/K, the rate of change
of the capital stock.
Investment rate (I/K)
(a)
MPKMarginal return of new investment
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Figure 6.17
Fig. 6.17
Tobins q when adjustment costs are significant
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.
Present value of MPK,cost of capital
Investment rate (I/K)
(a)
MPKMarginal return of new investment
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Figure 6.17
Fig. 6.17
Tobins q
With the investment rate corresponding to the
rate at point A, in the following period there
will be more capital and a lower MPK.
Marginal cost of investment
Present value of MPK,cost of capital
A
The investment rate next period will fall too (as
will Tobins q), ultimately heading toward a
value of unity and no more investment.
1
MPK1
Investment rate (I/K)
(b)
MPKMarginal return of new investment
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Tobins 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.

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Empirics (Contd)

• 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).

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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 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.

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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.