1

Investment in Business Cycle Models

Miles Kimball

2

The Power of Investment in Business Cycle Models

I. 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”

II. 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 W=Cv’(N), or equivalently, N=v’-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-α) / (C/Y).

1-α is labor’s 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)

5

Sector-Specific Technical Change

Susanto BasuBoston College and NBER

Jonas Fisher Federal Reserve Bank of Chicago

John FernaldFederal Reserve Bank of San

Francisco

Miles Kimball University of Michigan and NBER

Very preliminary

6

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 prices

might not measure technology correctly

• Top down versus bottom up

7

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

8

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.

9

Consider social-planners problem for two-sector growth model, with CRS, identical production technologies

0, , ,

0

1

max [ln( ) ( )]

. . ( , )

( , )

,

(1 )

tt t

N C X It

C N

I I

C I C I

t t t

E C v N

s t C AZ F K N

I Z F K N

K K K N N N

K I K

10

This is Special Case of Following, Simple Social Planner’s Problem

0, , ,

0

1

max [ln( ) ( )]

. .

( , , )

(1 )

tt t

N C X It

t t t

t t t

E C v N

s t C A X

X I G F K N Z

K I K

0, ,

0

1

max [ln( ) ln( ) ( )]

. . ( , , )

(1 )

tt t t

N X It

t t t t t t

t t t

E A X v N

s t X I G F K N Z

K I K

Equivalent problem:

11

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.

12

King-Plosser-Rebelo Utility with EIS < 1 (γ>1)

1

0, , ,

0

1

( )max

1

. .

( , , )

(1 )

t t t

C I N Xt

t t t

t t t

C NE

s t C A X

X I G F K N Z

K I K

1 11

0 0, , , 00

1

( )max

1

. . ( , , )

(1 )

t t tt

C I N Xt

t t t t t t

t t t

X NAA E A

s t X I G F K N Z

K I K

Equivalent problem:

13

An Example: Mean-Reverting Consumption Technology

• If A follows an AR(1) process, then At /A0 < 1 after an increase in A above the steady-state level at time zero.

• This makes (At /A0)1-γ > 1, which has the same effect as if

the discount factor β were larger. • Higher β (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 < 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, C=AX may increase even though X decreases.

14

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.

15

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.

16

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.

17

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 (EIS<1and 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 economy—the 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 special—for one thing, it has very different trend growth

19

Terms of Trade as Technology, cont’d

• Thus, need to allow ToT to follow a different stochastic process than more conventional technical change

• Ultimately a definitional question:Should ‘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

Rearrangement in terms of "supply":

t t t

Supply Supply Domestictt t t t tB Y C J G NX Y Y M

��������������

where is ( 1) ( 1), all other variables are ( 1) 1tB n n n

The (n+1)'th sector is "trade". We include "exports" as

an intermediate input into producing "trade goods" (imports plus NX).

The NX column is zeros except for row ( 1)n

Standard input-output table for commodities:

t t

Supply Domestict tt t tt

n

A Y C J G X M Y ��������������

22

Defining final-use technology

1

Rearranging yields:

[ ]t

Supplytt t t tY I B C J G NX

��������������

Ci

t

For industry , define final-use "column shares", e.g.,

b / ,where

sum(C ).

it t

t

i

C C

C

1 Commodity

1 Commodity

1 Commodity

1 Commodity

We define final-use technology as:

[ ]

[ ]

[ ]

[ ]

CC t

JJ t

GG t

TradeTrade t

dz b I B dz

dz b I B dz

dz b I B dz

dz b I B dz

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

24

The Power of Investment in Business Cycle Models

I. 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”

II. 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)

25

26

-4 0 4 8 160.4

0.6

0.8

1

1.2

1.4

Starts-4 0 4 8 16

0.9

0.95

1

1.05

1.1

1.15

real nonduruablesdef

Romer dateTrend

-4 0 4 8 160.8

0.9

1

1.1

1.2

1.3

real durablesdef

-4 0 4 8 160.9

0.95

1

1.05

1.1

1.15

real GDPdef

-4 0 4 8 160.6

0.8

1

1.2

Real Res Investmentdef

-4 0 4 8 160.6

0.8

1

1.2

real autocpi

Average Response of Real Production Following a Romer Date

27

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.

28

-4 0 4 8 12 160.8

0.85

0.9

0.95

1

1.05

1.1

1.15

Avg House pr / CPI nondur-4 0 4 8 12 16

0.85

0.9

0.95

1

1.05

1.1

Med House pr/ CPI nondur

-4 0 4 8 12 160.92

0.94

0.96

0.98

1

1.02

1.04

CPI durables/ CPI nondur-4 0 4 8 12 16

0.9

0.95

1

1.05

CPI cars/ CPI nondur

Average Response of Relative Prices Following a Romer Date

29

30

31

32

33

34

35

36

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/δ.

2. Only the first few terms in this series will be affected.

37

Consider a durable good with flexible prices

' tt jt

jt

Wv N

P

Nd: Wt/Pjt=MRPN=f(Nt)/μj

The Neutrality Problem

Ns:

Labor Market Equilibrium:v’(Nt) = (γjt/μj)f(Nt) ≈ (γj/μj)f(Nt)

38

The Comovement Problem

v’(Nt) ≈ (γj/μj)fj(Njt)

39

The Quantity of Nondurables Is Slaved to the Relative Price

40

41

The Power of Durables

42

The Power of Investment in Business Cycle Models

I. 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”

II. 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)

43

44

Note--Opposite Slope for a Wicksellian Rule: r=by y + bπ π + bx(x-p), where x is the price target.

LM Curve Case

45

46

Real Rigidity and the Dynamics of Inflation

47

The Dynamics of Inflation (θ=Calvo Parameter)

dπ/dt= - θ2 β(y-yf)

Compare toπt= πe

t+1 + θ(θ+r*)β(y-yf)

48

dπ/dt= - θ2 β(y-yf)(θ=Calvo Parameter)

49

Investment is the Key to the Determination of y

50

Cost MinimizationRK/WN=α/(1-α)Thus: R-δ = [α/(1-α)] (WN/K) – δ

Neoclassical labor supplyWN/K = Ws(N(Y,K,Z),λ) N(Y,K,Z)/K where λ is the marginal value of wealth

51

52

dπ/dt= - θ2 β(y-yf)

53

54

Note—dπ/dt has opposite slope for Wicksellian rule: r=by y + bπ π + bx(x-p).Saddle path has same slope.

LM Curve Case

55

56

57

58

A Positive Labor Supply Shock

59

R-δ = [α/(1-α)] (Ws(N)N/K) – δ

60

61

LM shifts back, then gradually out, going beyond its initial position.If dπ/dt slopes the other way because of a Wicksellian rule instead of an LM curve, the monetary policy rule will jump out, then graduallyshift out further.

62

63

A Technology Shock

64

Catastrophic Collapse of Investment and the Great Depression

Robert Barsky

Miles KimballUniversity 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-theoretic 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 didn’t 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 wasn’t 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 (don’t confuse

impulse with propagation!)• Bernanke a partial exception

• But emphasis is on financing, not implications of investment per se

70

The Net Rental Rate

•r=R-δ •N=Y1/γ(1-α)K-α/(1-α)Z-1 (IRTS Cobb Douglas production function)•RK/WN=α/(1-α) (constant cost shares )•W=–UN/UC = W(N(Y,K,Z),λ) (labor

supply)

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

71

Y

r

The Net Rental Rate Curve

r=0–

NRR

Ymin

(I=Imin)

Note: Curve would be steeper if elasticity of substitution between K and L were less than unity

•Recall that both N and W are increasing in Y

Here gross investment is zero (or at some fixed minimum)

•Low Y → low of Investment

72

Wage Bill

700

750

800

850

900

950

1000

1925 1930 1935 1940 1945

TOTWAGESAL/DEFLATOR

Total Real Wage and Salary Payments

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

73

Gross Investment CollapseGross Investment Collapse

0

5

10

15

20

25

30

35

24 26 28 30 32 34 36 38 40 42 44 46

GROSSCAPFORM_REAL

-8

-4

0

4

8

12

24 26 28 30 32 34 36 38 40 42 44 46

NETCAPFORM_REAL

2

4

6

8

10

12

14

24 26 28 30 32 34 36 38 40 42 44 46

New Manufacturing Capital Expenditure, Real

74

Gross Investment Collapse: Building Index and Building Permits

0

50

100

150

200

250

300

1925 1930 1935 1940 1945

BUILDING_TOT_INDEX

0

100

200

300

400

1925 1930 1935 1940 1945

Building Permits, Chicago

0

40

80

120

160

200

1925 1930 1935 1940 1945

BUILDPERM_SC_IND

0

40

80

120

160

200

1925 1930 1935 1940 1945

BUILDPERMIT_REAL

75

Y

r Multiple Short Run Equilibria

MP

–πe

r=0–

Ymin

(I=Imin)

Ynatural

NRR

Selection Criterion: Stay put unless the equilibrium you are at disappears

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?

77

Y

r Unexpected Monetary Contraction

MP

–πr=0–

Ymin

(I=Imin)

NRR

78

Y

r Expected DeflationMP

–πr=0–

Ymin

(I=Imin)

Ynatural

NRR

79

Y

r Hysteresis: A Monetary Restoration May Not Restore the Original Equilibrium

MP

–πr=0–

Ymin

(I=Imin)

Ynatural

NRR

80

Y

r Further, Modest Monetary or Fiscal Expansions Provide No Escape

Ymin

(I=Imin)

MP

–πr=0–

Monetary Expansion Shifts MP Right or Down

Fiscal Expansion Shifts Ymin Right

NRR

81

Y

r An Escape by Monetary Policy Alone Can Cause a Jump Above the Natural Level of Output

MP

–πr=0–

Ymin

(I=Imin)

Ynatural

NRR

82

Y

r The Skillful Way Out Involves a Monetary Restoration Plus a Fiscal Expansion

MP

–πr=0–

Ymin’=C+Imin+G’ Ynatural

NRR

83

Endogenizing Inflation: The Phase Diagram in the Neighborhood of the Steady State in the Absence of an Investment Collapse

x (real moneybalances)

steady-stateinflation

dx/dt =0

dπ/dt =0 π=0(different positions possible)

π

84

The Phase Diagram with Coexisting Blue (Normal) and Red (Depression) Dynamics Shown

x (real moneybalances)

steady-stateinflation

dx/dt =0

dπ/dt =0 π=0(different positions possible)

Collapse Boundary

π

ReignitionBoundary

85

The Phase Diagram with Only the Blue (Normal) and Red (Depression) Saddle Paths Shown

x (real moneybalances)

steady-stateinflation

dx/dt =0

dπ/dt =0 π=0(different positions possible)

Collapse Boundary

π

collapse values of x

ReignitionBoundary

Assume log money follows random walk with constant drift

86

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

x (real moneybalances)

steady-stateinflation

dx/dt =0

dπ/dt =0 π=0(different positions possible)

Collapse Boundary

π

collapse values of x

ReignitionBoundary

•Moves boundary to left of of p-dot=0 locus

•Avoids need for inflationary boom

88

The Power of Investment in Business Cycle Models

I. 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”

II. 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)