Investment in Business Cycle Models

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Investment in Business Cycle Models

• Miles Kimball

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The Power of Investment in Business Cycle Models

• The technology-induced fluctuations in standard
  Real Business Cycle models are fundamentally
  investment booms.
• Kimball and Ramnath With Realistic Parameters
  the Basic Real Business Cycle model Acts Like the
  Solow Growth Model
• Basu, Fernald, Fisher and Kimball
  Sector-Specific Technology Shocks
• Including investment dramatically changes the
  behavior of sticky-price models.
• Barsky, House, and Kimball Durable Goods and
  Sticky-Price Models
• III. The Neomonetarist Synthesis (Kimball)
• IV. A catastrophic collapse of investment was a
  key propagation mechanism for the Great
  Depression. (Barsky and Kimball)

3
With Realistic Parameters the Basic Real
Business Cycle Model Acts Like the Solow Growth
Model

• To match the lack of strong long-run trend in
  labor hours, Real Business Cycle models need
  King-Plosser-Rebelo preferences, engineered to
  get WCv(N), or equivalently, Nv-1(W/C).
• Technology shocks are permanent.
• --A priori argument Useful knowledge not soon
  forgotten
• --Direct evidence from Are Technology
  Improvements Contractionary? by Basu, Fernald
  and Kimball
• The elasticity of intertemporal substitution is
  low.
• --Consumption Euler equation evidence (Hall)
• --Hypothetical choice evidence (Kimball, Sahm and
  Shapiro)

4
With Realistic Parameters the Basic Real
Business Cycle Model Acts Like the Solow Growth
Model

• Given King-Plosser-Rebelo preferences with an
  elasticity of intertemporal substitution of about
  0.3, permanent technology shocks have essentially
  no effect on I/Y or N.
• These two results are linked. Multiply Cv(N)W
  by N/C
• Nv(N) WN/C (WN/Y) / (C/Y)
  (1-a) / (C/Y).
• 1-a is labors share. Given Cobb-Douglas, N
  depends only on C/Y (negatively). Note that C/Y
  1-(I/Y)-(G/Y).
• Thus, N will increase only if I/Y or G/Y
  increases if a tech shock does not induce an
  investment boom, it does not raise labor hours.
• Instead, output and investment go up by the same
  percentage due to the direct effect of the
  technology shock, and capital accumulates. (Same
  as the response of Solow Growth Model to a perm.
  tech shock)

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Sector-Specific Technical Change

• Susanto Basu
• Boston College and NBER
• Jonas Fisher
• Federal Reserve Bank of Chicago

John Fernald Federal Reserve Bank of San
Francisco Miles Kimball University of Michigan
and NBER
Very preliminary
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Where does growth originate?

• Technical change differs across industries
• Recent work has highlighted that the final-use
  sector in which technical change occurs matters
• Greenwood, Hercowitz, Krusell
• Use relative price data
• We reconsider the evidence
• Extending GHK to situations where relative
  pricesmight not measure technology correctly
• Top down versus bottom up

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Outline

• Motivation Consumption-technology neutrality
• How to think about terms of trade?
• Disaggregating Manipulating the input-output
  matrix
• Comparing bottom-up versus top-down estimates

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Consumption Technology Neutrality

• Suppose utility is logarithmic
• Suppose there is some multiplicative technology A
  for producing non-durable consumption goods
• The stochastic process for consumption-technology
  A affects only the production of nondurable
  consumption goods
• It does not affect affect labor hours N,
  investment I, or an index of the resources
  devoted to producing consumption goods X.

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Consider social-planners problem for two-sector
growth model, with CRS, identical production
technologies
10
This is Special Case of Following, Simple Social
Planners Problem
Equivalent problem
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Comments

• Because ln(A) is an additively-separable term,
  any stochastic process for A has no effect on the
  optimal decision rules for N, X and I.
• There is a weaker, but still important result for
  the more general King-Plosser-Rebelo case
• anticipated movements in A act like changes in
  the utility discount rate
• unanticipated movements in A have no effect on
  the optimal decision rules for N, X and I.

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King-Plosser-Rebelo Utility with EIS lt 1 (?gt1)
Equivalent problem
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An Example Mean-Reverting Consumption
Technology

• If A follows an AR(1) process, then At /A0 lt 1
  after an increase in A above the steady-state
  level at time zero.
• This makes (At /A0)1-? gt 1, which has the same
  effect as if the discount factor ß were larger.
• Higher ß (greater patience) would lead to an
  increase in investment I, an increase in labor
  hours N, and a reduction in the resources devoted
  to consumption X.
• Thus, At /A0 lt 1 leads to an increase in
  investment I, an increase in labor hours N, and a
  reduction in the resources devoted to consumption
  X.
• However, CAX may increase even though X
  decreases.

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Empirical Implications Standard RBC Parameters

• With the standard parametrizations of the utility
  function consumption technology shocks will have
  very different effects from investment technology
  shocks.
• consumption technology shocks have no effect on
  labor hours or investment.
• investment technology shocks have the same effect
  on labor hours and investment as pervasive
  technology shocks.
• therefore, like pervasive technology shocks in
  standard RBC models, investment technology shocks
  should have a large effect on labor hours and
  investment.

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Empirical Implications Low EIS and Permanent
Tech Shocks

• With permanent technology shocks and
  King-Plosser-Rebelo utility and relatively low
  elasticity of intertemporal substitution ( 0.3),
  investment technology shocks also have very
  little immediate effects on labor hours, though
  they do raise investment in a way that
  consumption technology shocks do not.

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A More General Question

• Example of consumption technology neutrality
  raises possibility that shocks to different final
  sectors have different effects on aggregate labor
  hours and investment.
• Therefore, we would like to construct technology
  shocks for goods of different levels of
  durability to see empirically if these have
  different effects.

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Motivation A novel test of price stickiness

• In the log case, a change in consumption
  technology should have no effect on investment
  and hours
• For plausible deviations from log utility of
  consumption and permanent technology shocks
  (EISlt1and AR(1) technology as analyzed above),
  improvements in consumption technology should
  raise investment
• But with sticky prices, Basu-Kimball (2001) show
  that improved consumption technology should lower
  investment and hours in the short run
• Reason is that with price stickiness, relative
  price of consumption cannot jump down on impact
• However, consumption technology should have
  RBC-style effect once effective price stickiness
  ends

18
Terms of Trade as Technology

• In a closed economy, relative prices are always
  driven by domestic factors, including domestic
  technology
• But this is not true with an open economythe
  relative price faced by a small open economy can
  change due to changes in foreign technology or
  demand
• We classify such price changes as technology
  shocks because they enable home consumers to
  have more consumption with unchanged labor input
• View trade as a special (linear) technology, with
  terms of trade changes as technology shocks
• However, this type of technology is specialfor
  one thing, it has very different trend growth

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Terms of Trade as Technology, contd

• Thus, need to allow ToT to follow a different
  stochastic process than more conventional
  technical change
• Ultimately a definitional questionShould
  technology represent a change in the
  possibility frontier for consumption and leisure,
  or be restricted to a change in the production
  functions for domestic C and I?
• We use the first, broader, definition. Labeling
  does not matter, so long as one takes into
  account both ToT changes and domestic PF shifts

20
Issues in using industry/commodity data to
measure sectoral technical change

• Final use is by commodity, productivity data are
  by industry
• I-O make table maps commodity production to
  industries
• Can translate industry technology into final-use
  technology, using
• dzCommodity M-1dzIndustry,
• where dzIndustry is vector of industry
  technologies
• Industry/commodity TFP is in terms of domestic
  production, whereas final-use reflects total
  commodity supply
• Domestic commodity production plus commodity
  imports
• I-O use table tells us both production and
  imports
• Requires rescaling domestic-commodity technology

21
Rearranging the standard input-output table
22
Defining final-use technology
23
Notes

• Trade technology is the terms of trade
• Suppose there are no intermediate-inputs and one
  of each final-use commodity (e.g., a single
  consumption good)
• Final-use technology is technology in that
  commodity
• Otherwise, takes account of intermediate-input
  flows

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The Power of Investment in Business Cycle Models

• The technology-induced fluctuations in standard
  Real Business Cycle models are fundamentally
  investment booms.
• Kimball and Ramnath With Realistic Parameters
  the Basic Real Business Cycle model Acts Like the
  Solow Growth Model
• Basu, Fernald, Fisher and Kimball
  Sector-Specific Technology Shocks
• Including investment dramatically changes the
  behavior of sticky-price models.
• Barsky, House, and Kimball Durable Goods and
  Sticky-Price Models
• III. The Neomonetarist Synthesis (Kimball)
• IV. A catastrophic collapse of investment was a
  key propagation mechanism for the Great
  Depression. (Barsky and Kimball)

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There Must Be Sticky Prices for Durables to Get
This Kind of Behavior

• We show that if a durable goods have flexible
  prices, a monetary contraction will raise the
  output of that durable.
• Durability, not final use is the key feature for
  this point, business investment, housing
  investment and other long-lived durable purchases
  are similar.

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The Marginal Value of a Durable is Largely
Invariant to Shocks with Temporary Real Effects
1. Stocks of durables will change slowly because
of a high stock/flow ratio 1/d. 2. Only the
first few terms in this series will be affected.

37
The Neutrality Problem
Nd Wt/PjtMRPNf(Nt)/µj
Consider a durable good with flexible prices
Ns
Labor Market Equilibrium v(Nt) (?jt/µj)f(Nt)
(?j/µj)f(Nt)
38
The Comovement Problem
v(Nt) (?j/µj)fj(Njt)
39
The Quantity of Nondurables Is Slaved to the
Relative Price
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The Power of Durables
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The Power of Investment in Business Cycle Models

• The technology-induced fluctuations in standard
  Real Business Cycle models are fundamentally
  investment booms.
• Kimball and Ramnath With Realistic Parameters
  the Basic Real Business Cycle model Acts Like the
  Solow Growth Model
• Basu, Fernald, Fisher and Kimball
  Sector-Specific Technology Shocks
• Including investment dramatically changes the
  behavior of sticky-price models.
• Barsky, House, and Kimball Durable Goods and
  Sticky-Price Models
• III. The Neomonetarist Synthesis Adding a
  Non-Zero Interest Elasticity of Money Demand to
  the Basic Neomonetarist Model (Kimball)
• IV. A catastrophic collapse of investment was a
  key propagation mechanism for the Great
  Depression. (Barsky and Kimball)

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LM Curve Case
Note--Opposite Slope for a Wicksellian Rule
rby y bp p bx(x-p), where x is
the price target.
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Real Rigidity and the Dynamics of Inflation
47
The Dynamics of Inflation (?Calvo Parameter)
dp/dt - ?2 ß(y-yf)
Compare to pt pet1 ?(?r)ß(y-yf)
48
dp/dt - ?2 ß(y-yf)
(?Calvo Parameter)
49
Investment is the Key to the Determination of y
50
Cost Minimization?RK/WNa/(1-a) Thus R-d
a/(1-a) (WN/K) d Neoclassical labor
supply? WN/K Ws(N(Y,K,Z),?) N(Y,K,Z)/K where ?
is the marginal value of wealth
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dp/dt - ?2 ß(y-yf)
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LM Curve Case
Notedp/dt has opposite slope for Wicksellian
rule rby y bp p bx(x-p). Saddle path has
same slope.
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A Positive Labor Supply Shock
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R-d a/(1-a) (Ws(N)N/K) d
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LM shifts back, then gradually out, going beyond
its initial position. If dp/dt slopes the other
way because of a Wicksellian rule instead of an
LM curve, the monetary policy rule will jump out,
then gradually shift out further.
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A Technology Shock
64
Catastrophic Collapse of Investment and the Great
Depression

• Robert Barsky
• Miles Kimball
• University of Michigan and NBER

Very preliminary discussion prepared for seminar
at Michigan, April 11, 2007. Please do not
circulate.
65
Executive Summary Model

• Study Great Depression in standard New Keynesian
  sticky price model with capital
• Provides interesting synthesis of
• Consensus monetary view of Depression emanating
  from Friedman and Schwartz
• with
• Earlier arch-Keynesian real theories based on
  collapse of investment, building cycles, floors
  and ceilings, self-fulfilling prophecies, etc.
• Has elements of the nonlinear, catastrophe-theoret
  ic development of the latter by Hicks, Kaldor,
  Goodwin, Kalecki, Varian, etc. but
• Money remains the driving variable
• Model is modern, recognizable, and totally
  standard

66
Executive Summary, cont. Empirical Facts

• Gross Investment really did collapse essentially
  to zero
• Sharp drop in wage bill
• Indicates sharp decline in rental rates on
  capital
• Strongly deflationary environment with very high
  real interest rates until 1933
• Then sharp turn towards inflation, low real rates
• Rental rates and investment didnt show strong
  recovery until at least 1935

67
Bottom Line Explanation of Depression and
Recovery

• Very high real rates confronted low rental rates
  on capital
• Former due to tight money and deflation
• Latter due both to low output and possibly high
  inherited capital stock
• This lead to complete investment collapse,
  apparently hitting between 1931 and 1932
• Turn toward inflation in 1933 plus depreciation
  of capital eventually reignites investment, but
  wasnt enough to do it quickly

68
Elements

• NRR curve net rental rate on capital
• MP curve real interest rate as function of
  output
• Easiest case LM curve from constant elasticity
  money demand function
• Phase diagram to endogenize inflation

69
When and Why Did Investment Leave Great
Depression Models?

• Friedman and Schwartz
• Persuasive
• Highly aggregative no discussion of components
  of GNP
• Emphasis on why money stock collapsed, not how it
  caused fall in output
• Temin
• Pointed out drop of gross investment to near-zero
  in 1932 but
• Found autonomous fall in consumption, not
  investment (dont confuse impulse with
  propagation!)
• Bernanke a partial exception
• But emphasis is on financing, not implications of
  investment per se

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The Net Rental Rate

• Rental Market for Capital (no adjustment costs,
  investment smoothing)
• Rental rate R marginal cost product of
  capital (sticky prices, demand-constrained

• rR-d
• NY1/?(1-a)K-a/(1-a)Z-1 (IRTS Cobb Douglas
  production function)
• RK/WNa/(1-a) (constant cost shares )
• WUN/UC W(N(Y,K,Z),?) (labor supply)

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r
The Net Rental Rate Curve

• Recall that both N and W are increasing in Y

• Low Y ? low of Investment

NRR
Note Curve would be steeper if elasticity of
substitution between K and L were less than unity
r0
Y
Here gross investment is zero (or at some fixed
minimum)
Ymin (IImin)
72
Wage Bill

• Capital essentially fixed over short period
• Indicator of Net Rental Rate

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Gross Investment Collapse
Gross Investment Collapse
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Gross Investment Collapse Building Index and
Building Permits
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r
Multiple Short Run Equilibria
MP
Selection Criterion Stay put unless the
equilibrium you are at disappears
NRR
r0
pe
Y
Ynatural
Ymin (IImin)
76
Depression Predisposing Factors From 1920s

• Low inflation or deflation (Makes MP curve high)
• Technology revolution
• Overbuilding? (Makes NRR curve low)
  -liquidationist" viewpoint
• Long expansionary period
• Easy money?
• Over-optimism about growth rates?

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r
Unexpected Monetary Contraction
MP
NRR
r0
p
Y
Ymin (IImin)
78
r
Expected Deflation
MP
NRR
p
r0
Y
Ynatural
Ymin (IImin)
79
Hysteresis A Monetary Restoration May Not
Restore the Original Equilibrium
r
MP
NRR
r0
p
Y
Ymin (IImin)
Ynatural
80
Further, Modest Monetary or Fiscal Expansions
Provide No Escape
r
MP
Monetary Expansion Shifts MP Right or Down
Fiscal Expansion Shifts Ymin Right
NRR
r0
p
Y
Ymin (IImin)
81
An Escape by Monetary Policy Alone Can
Cause a Jump Above the Natural Level of Output
r
MP
NRR
r0
p
Y
Ynatural
Ymin (IImin)
82
The Skillful Way Out Involves a Monetary
Restoration Plus a Fiscal Expansion
r
MP
NRR
r0
p
Y
Ynatural
YminCIminG
83
Endogenizing Inflation The Phase Diagram in
the Neighborhood of the Steady State in the
Absence of an Investment Collapse
p
steady- state inflation
dx/dt 0
p0 (different positions possible)
dp/dt 0
x (real money balances)
84
The Phase Diagram with Coexisting Blue (Normal)
and Red (Depression) Dynamics Shown
p
steady- state inflation
dx/dt 0
Reignition Boundary
p0 (different positions possible)
dp/dt 0
Collapse Boundary
x (real money balances)
85
The Phase Diagram with Only the Blue (Normal)
and Red (Depression) Saddle Paths Shown
p
Assume log money follows random walk with
constant drift
steady- state inflation
dx/dt 0
Reignition Boundary
p0 (different positions possible)
dp/dt 0
Collapse Boundary
x (real money balances)
collapse values of x
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Lessons From Phase Diagram

• Nonlinearity
• Need sufficiently large monetary expansion to get
  to the reignition boundary
• Nothing happens to investment and output until
  then
• Hysteresis
• Dynamics depend on where you start from
• Probably need inflationary boom to reach
  reignition region
• Mundell and Keynes effects
• Keynes effect will restore full-employment in
  long run
• Low but rising inflation means Mundell will
  eventually switch from harmful to helpful

87
Using a Fiscal Expansion to Shift the Reignition
Boundary
p

• Moves boundary to left of of p-dot0 locus
• Avoids need for inflationary boom

steady- state inflation
dx/dt 0
p0 (different positions possible)
dp/dt 0
x (real money balances)
collapse values of x
Reignition Boundary
Collapse Boundary
88
The Power of Investment in Business Cycle Models

• The technology-induced fluctuations in standard
  Real Business Cycle models are fundamentally
  investment booms.
• Kimball and Ramnath With Realistic Parameters
  the Basic Real Business Cycle model Acts Like the
  Solow Growth Model
• Basu, Fernald, Fisher and Kimball
  Sector-Specific Technology Shocks
• Including investment dramatically changes the
  behavior of sticky-price models.
• Barsky, House, and Kimball Durable Goods and
  Sticky-Price Models
• III. The Neomonetarist Synthesis (Kimball)
• IV. A catastrophic collapse of investment was a
  key propagation mechanism for the Great
  Depression. (Barsky and Kimball)