mrp beta slides

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Motivation Discounting Discounting Plant-Level Optimization Results

Do Interest Rates Smooth Investment?

Russell Cooper1 Jon Willis2 1_{Pennsylvania State University} 2_{Federal Reserve Bank of Kansas City}

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Question: How do variations in the interest rate influence

plant-level and aggregate investment?

The answer will improve our understanding of:

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Micro evidence

Investment at the plant level is characterized by infrequent adjustment.

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Micro evidence

Investment at the plant level is characterized by infrequent adjustment.

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Previous research

Research of Thomas (2002), Khan and Thomas (2003), and Khan and Thomas (2008) concludes that non-convexities at the plant level are not important for aggregate investment.

State dependent interest rates in these models are determined in equilibrium.

The striking result is the absence of aggregate effects of lumpy investment.

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Previous research

Research of Thomas (2002), Khan and Thomas (2003), and Khan and Thomas (2008) concludes that non-convexities at the plant level are not important for aggregate investment. State dependent interest rates in these models are determined in equilibrium.

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Previous research

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Previous research

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Our focus

In studying the investment decisions of establishments, what interest rate process are they responding to?

Our focus is studying the effects of interest rate movements found in the data.

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Our focus

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Our focus

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Key theme: Specifying an interest rate process

Why distinguish data-based interest rate process from model-based interest rate process?

Table: Interest rate properties

Std. dev. relative Correlation to output with output

Data .444 -.385

Benchmark (RBC) .096 .889

State-dependent adjustment .095 .892

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Roadmap for presentation

1 _{Model with non-convex adjustment costs for investment} 2 _{Specify interest rate process (state dependent discount factor)} 3 Specify aggregate process: detrending specification has strong

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Results

Plant-level moments used to estimate parameters in PE studies are insensitive to interest rate process

Specification of interest rate process strongly influences plant-level and aggregate investment response to shocks Specification of aggregate shock process strongly influences the responsiveness of investment to aggregate shock Observed extensive margin of investment behavior supports data-based interest rate process

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Results

Specification of interest rate process strongly influences plant-level and aggregate investment response to shocks

Specification of aggregate shock process strongly influences the responsiveness of investment to aggregate shock Observed extensive margin of investment behavior supports data-based interest rate process

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Results

Specification of interest rate process strongly influences plant-level and aggregate investment response to shocks Specification of aggregate shock process strongly influences the responsiveness of investment to aggregate shock

Observed extensive margin of investment behavior supports data-based interest rate process

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Results

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Results

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Results

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Our Approach

1 Decentralized solution for establishment’s problem with empirically consistent

State dependent discounting

Adjustment costs for investment

Heterogeneity in productivity

Monopolistic competition

Use equilibrium prices instead of planner’s problem

2 To study:

Smoothing effects of state-dependent discounting

Effects of variation in the interest rate on plant-level and

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Our Approach

1 Decentralized solution for establishment’s problem with empirically consistent

State dependent discounting

Adjustment costs for investment

Heterogeneity in productivity

Monopolistic competition

Use equilibrium prices instead of planner’s problem

2 To study:

Smoothing effects of state-dependent discounting

Effects of variation in the interest rate on plant-level and

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State-Dependent Discount Factor (SDDF)

Household optimization for any asset j: Et h

˜

βt+1R_tj₊₁

i

= 1

Asset pricing kernel: ˜βt+1= βU

0₍_C t+1)

U0₍_C t)

Establishment-level problem (stationary):

V(A, ε,k,Z) = max

k0

π(A, ε,k)−C(A, ε,k,k0) +

E_A0_,Z0_,ε0_|_A,Z_,ε[ ˜β(·)V(A0, ε0,k0,Z0)] o

Monetary Policy targets R_tM₊₁ conditional onZt andZt+1

Impacts Euler Equation

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State-Dependent Discount Factor (SDDF)

˜

βt+1R_tj₊₁

i

= 1 Asset pricing kernel: ˜βt+1= βU

0₍_C t+1)

U0₍_C t)

V(A, ε,k,Z) = max

k0

π(A, ε,k)−C(A, ε,k,k0) +

E_A0_,Z0_,ε0_|_A,Z_,ε[ ˜β(·)V(A0, ε0,k0,Z0)] o

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State-Dependent Discount Factor (SDDF)

˜

βt+1R_tj₊₁

i

0₍_C t+1)

U0₍_C t)

V(A, ε,k,Z) = max

k0

π(A, ε,k)−C(A, ε,k,k0) +

E_A0_,Z0_,ε0_|_A,Z_,ε[ ˜β(·)V(A0, ε0,k0,Z0)] o

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State-Dependent Discount Factor (SDDF)

˜

βt+1R_tj₊₁

i

0₍_C t+1)

U0₍_C t)

V(A, ε,k,Z) = max

k0

π(A, ε,k)−C(A, ε,k,k0) +

E_A0_,Z0_,ε0_|_A,Z_,ε[ ˜β(·)V(A0, ε0,k0,Z0)] o

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Issues

Asset Pricing

Can we rely on the HH Euler equation to price assets, including investment and the federal funds market?

Canzoneri et al. (2007) find huge differences between money market rates and (parameterized) HH Euler equations. Is this the right channel for monetary policy?

What are the adjustment costs at the plant-level?

Cooper and Haltiwanger (2006)

Includes market power and heterogeneity

Check moment implications with state dependent discounting

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Issues

Asset Pricing

Canzoneri et al. (2007) find huge differences between money market rates and (parameterized) HH Euler equations.

Is this the right channel for monetary policy?

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Issues

Asset Pricing

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Issues

Asset Pricing

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Issues

Asset Pricing

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What interest rate should be used to discount plant level profits?

1 Model Based:

Interest rate derived from general equilibrium model (Thomas

(2002), Khan and Thomas (2003), and others)

Mapping from states to interest rates determined within model

2 _{Data Based:}

Estimate functional relationship between Euler-equation-based

discount rate and aggregate state variables

Coefficients from data not model

3 Estimate state-dependent market rates directly

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1 Model Based:

2 _{Data Based:}

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1 Model Based:

2 _{Data Based:}

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1 Model Based:

2 _{Data Based:}

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Finding the pricing kernel: ˜

β

=

B

(

·

)

Use the Data

1 _{Calculate ˜}_β_t+1₌βU

0_(C t+1) U0_(C

t) from data

2 _Specify_B₍·₎

3 _{Estimate it from aggregate data}

Use a Model

1 _{Stochastic Growth Model with Monopolistic Competition (eg.}

Chatterjee and Cooper (1993))

2 _Ct₌_C₍_At_,_Kt_),_Kt+1₌_K₍_At_,_Kt_{) , ˜}_β_t+1₌ βU

0_(C t+1) U0_(C_t₎

3 ₍_A_,_K_{) are aggregate state variables}

4 _{Solve model and obtain evolution of states and controls to}

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Finding the pricing kernel: ˜

β

=

B

(

·

)

Use the Data

1 _{Calculate ˜}_β_t+1₌βU

0_(C t+1) U0_(C

t) from data

2 _Specify_B₍·₎

3 _{Estimate it from aggregate data}

Use a Model

1 _{Stochastic Growth Model with Monopolistic Competition (eg.}

Chatterjee and Cooper (1993))

2 _Ct₌_C₍_At_,_Kt_),_Kt+1₌_K₍_At_,_Kt_{) , ˜}_β_t+1₌ βU

0_(C t+1) U0_(C_t₎

3 ₍_A_,_K_{) are aggregate state variables}

4 _{Solve model and obtain evolution of states and controls to}

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Estimating

B

(

A

t

,

A

t+1

,

K

t

)

Data: follow Stock and Watson (1999)

Consumption = Nondurables + Services (BEA)

Output = Real Business Nonfarm GDP (BEA)

Labor = Private nonfarm payroll employment (BLS)

Capital = Real private nonresidential fixed capital stock (BEA)

log(A) = log(Output) - 0.65*log(Labor) - 0.35*log(Capital)

Details:

Annual data from 1948 - 2008

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Estimating

B

(

A

t

,

A

t+1

,

K

t

)

Data: follow Stock and Watson (1999)

Consumption = Nondurables + Services (BEA)

Output = Real Business Nonfarm GDP (BEA)

Labor = Private nonfarm payroll employment (BLS)

Capital = Real private nonresidential fixed capital stock (BEA)

log(A) = log(Output) - 0.65*log(Labor) - 0.35*log(Capital)

Details:

Annual data from 1948 - 2008

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Estimating

B

(

A

t

,

A

t+1

,

K

t

)

1 _{Construct ˜}_βt₊₁₌ βU

0₍_C t+1)

U0₍_C

t) using U(C) =log(C) and β = 0.96

2 Regress ˜βt₊₁ on{A_t,A_t₊₁,K_t}

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Side Note: Filtering the data

1940 1950 1960 1970 1980 1990 2000 2010

−1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 Solow residual log level

1940 1950 1960 1970 1980 1990 2000 2010

−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1

Filtered Solow residual

log deviation from trend

! = 0.84

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Side Note: Filtering the data

−11940 1950 1960 1970 1980 1990 2000 2010

−0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 Solow residual log level

1940 1950 1960 1970 1980 1990 2000 2010

−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1

! = 0.84

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Side Note: Filtering the data

1940 1950 1960 1970 1980 1990 2000 2010

−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1

Filtered Solow residuals

! = 0.84

! = 0.14

Linear filter ("=100000) Band Pass filter (" = 7)

1940 1950 1960 1970 1980 1990 2000 2010

−0.15 −0.1 −0.05 0 0.05 0.1 0.15

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Pricing kernel (SDDF): ˜

β

=

B

(

A

t

,

A

t+1

,

K

t

)

Source At At+1 Kt R2 dEt_dA[ ˜β_t(·)]

Case 1 Data 0.34 -0.46 0.01 0.56 -0.04

λ= 100000 (0.05) (0.06) (0.03)

(ρA = 0.84) Chat-Coop 0.43 -0.64 0.09 NA -0.11

KPR 0.37 -0.59 0.09 NA -0.12

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Pricing kernel (SDDF): ˜

β

=

B

(

A

t

,

A

t+1

,

K

t

)

Case 1 Data 0.34 -0.46 0.01 0.56 -0.04

λ= 100000 (0.05) (0.06) (0.03)

(ρA = 0.84) Chat-Coop 0.43 -0.64 0.09 NA -0.11

KPR 0.37 -0.59 0.09 NA -0.12

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Pricing kernel (SDDF): ˜

β

=

B

(

A

t

,

A

t+1

,

K

t

)

Case 1 Data 0.34 -0.46 0.01 0.56 -0.04

λ= 100000 (0.05) (0.06) (0.03)

(ρA = 0.84) Chat-Coop 0.43 -0.64 0.09 NA -0.11

KPR 0.37 -0.59 0.09 NA -0.12

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Pricing kernel (SDDF): ˜

β

=

B

(

A

t

,

A

t+1

,

K

t

)

Case 1 Data 0.34 -0.46 0.01 0.56 -0.04

λ= 100000 (0.05) (0.06) (0.03)

(ρA = 0.84) Chat-Coop 0.43 -0.64 0.09 NA -0.11

KPR 0.37 -0.59 0.09 NA -0.12

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Pricing kernel (SDDF): ˜

β

=

B

(

A

t

,

A

t+1

,

K

t

)

Case 3 Data 0.20 -0.59 0.06 0.46 0.12

λ= 7 (0.09) (0.10) (0.15)

(ρA = 0.14) Chat-Coop 0.09 -0.41 0.09 NA 0.03

KPR 0.08 -0.39 0.09 NA 0.03

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Pricing kernel (SDDF): ˜

β

=

B

(

A

t

,

A

t+1

,

K

t

)

Case 3 Data 0.20 -0.59 0.06 0.46 0.12

λ= 7 (0.09) (0.10) (0.15)

(ρA = 0.14) Chat-Coop 0.09 -0.41 0.09 NA 0.03

KPR 0.08 -0.39 0.09 NA 0.03

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State-Dependent Discount Factor (SDDF)

−4₀ ₅ ₁₀ ₁₅ ₂₀ ₂₅ ₃₀ ₃₅ ₄₀ ₄₅ ₅₀ −2

0 2 4

Aggregate shock and expected discount factor (E[!]) when "_A = 0.14

periods (years)

percentage log deviation from steady state

0 5 10 15 20 25 30 35 40 45 50−0.4

−0.2 0 0.2 0.4

Aggregate profitability shock (left axis) Empirical discount factor (right axis) Chat−Coop discount factor (right axis)

0 5 10 15 20 25 30 35 40 45 50

−6 −4 −2 0 2 4 6

periods (years)

0 5 10 15 20 25 30 35 40 45 50−0.6

−0.4 −0.2 0 0.2 0.4 0.6

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Stochastic Discount Factor

0 5 10 15 20 25 30 35 40 45 50

−4

−2 0 2 4

periods (years)

0 5 10 15 20 25 30 35 40 45 50−0.4

−0.2 0 0.2 0.4

Aggregate profitability shock (left axis) Empirical discount factor (right axis) Chat−Coop discount factor (right axis)

0 5 10 15 20 25 30 35 40 45 50

−6 −4 −2 0 2 4 6

periods (years)

0 5 10 15 20 25 30 35 40 45 50−0.6

−0.4 −0.2 0 0.2 0.4 0.6

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Experiments

Questions

1 _{What are the effects of interest rates on aggregate and} plant-level investment?

2 _{Is there smoothing of nonconvexities through state-dependent} discounting?

Study by comparing outcomes

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Experiments

Questions

1 _{What are the effects of interest rates on aggregate and} plant-level investment?

2 _{Is there smoothing of nonconvexities through state-dependent} discounting?

Study by comparing outcomes

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Plant-Level Optimization Problem

V(A, ,k) = max{Vi(A, ε,k),Va(A, ε,k)}, ∀(A, ε,k),

where

Vi(A, ε,k) = Π(A, ε,k) +EA0_,ε0_|_A_,ε

h

˜

βV(A0, ε0,k(1−δ))i

Va(A, ε,k) = max

k0 Π(A, ε

0_,_k₎₋_C₍_A_{, ε,}_k_,_k0_{) +}

EA0_,ε0_|_A_,ε

h

˜

βV(A0, ε0,k0)i

where

C(A, ε,k,k0) =

disruption cost

z }| {

(1−λ) Π(A, ε0,k) +pb(I>0)(k0−(1−δ)k)

−ps(I<0)((1−δ)k−k0)

| {z }

irreversibility

+ν 2

k0₋₍₁₋_δ₎_k k

2 k

| {z }

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Three forms of investment adjustment costs:

disruption cost (λ)

quadratic adjustment cost (ν)

irreversibility (ps)

Estimate {λ, ν,ps} via SMM

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Parameters:

From CH (2006)

λ= 0.8

ν = 0.15

ps =0.98 ρε = 0.88

σε = 0.1

Constant returns to scale

θ = 5

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State Dependent Discounting and Plant-Level Investment

Plant-level moments used in CH (2006) estimation are insensitive to ˜β

Table: Plant-level moments

Model Corr(i,i−1) Corr(i, ε) Spike + Spike

-β -0.13 0.19 0.13 0

˜

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Plant-level investment regression on simulated data:

I

i

(

A

, ε

i

,

K

i

)

Model ρA A εi Ki R2

β 0.14 -12.78 28.47 -0.46 0.36

(3.22) (0.26) (0.00)

0.84 23.59 29.82 -0.43 0.36

(1.37) (0.27) (0.00)

˜

β(At,At+1) 0.14 24.58 28.40 -0.46 0.36

(Empirical) (3.22) (0.26) (0.00)

0.84 13.76 29.74 -0.43 0.36

(1.37) (0.27) (0.00)

˜

β(At,At+1) 0.14 -1.97 28.63 -0.46 0.36

(Chat-Coop) (3.21) (0.26) (0.00)

0.84 -6.48 30.20 -0.44 0.36

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Intensive margin

Table:Plant-level investment regression (Adjusters only):Ii(A, εi,Ki)

β 0.14 4.54 25.54 0.02 0.90

(2.57) (0.45) (0.01)

0.84 26.11 29.58 0.02 0.98

(0.56) (0.23) (0.01) ˜

β(At,At+1) 0.14 17.11 24.60 0.04 0.90

(Empirical) (2.59) (0.45) (0.01)

0.84 18.42 29.61 0.03 0.98

(0.50) (0.21) (0.00) ˜

β(At,At+1) 0.14 5.28 25.25 0.03 0.90

(Chat-Coop) (2.51) (0.44) (0.01)

0.84 2.80 29.67 0.03 0.99

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Extensive margin

Table:Linear probability regression using plant-level simulated data (extensive

margin)

β 0.14 -0.67 1.25 -0.84 0.37

(0.15) (0.01) (0.01)

0.84 1.00 1.26 -0.81 0.37

(0.06) (0.01) (0.01) ˜

β(At,At+1) 0.14 1.17 1.25 -0.84 0.37

(Empirical) (0.15) (0.01) (0.01)

0.84 0.58 1.24 -0.79 0.37

(0.06) (0.01) (0.01) ˜

β(At,At+1) 0.14 -0.11 1.26 -0.85 0.37

(Chat-Coop) (0.15) (0.01) (0.01)

0.84 -0.33 1.27 -0.81 0.37

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Aggregate Investment

0 5 10 15 20 25 30

−0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 periods (years)

deviation from mean

Aggregate shock and aggregate investment rate (I/K) when !_A = 0.14

0 5 10 15 20 25 30−0.03

−0.02 −0.01 0 0.01 0.02 0.03 0.04

deviation from mean

Aggregate profitability shock (left axis) Investment rate (fixed ") (right axis)

0 5 10 15 20 25 30

−0.06 −0.03 0 0.03 0.06 0.09

periods (years)

deviation from mean

0 5 10 15 20 25 30−0.04

−0.02 0 0.02 0.04 0.06

deviation from mean

(61)

Aggregate Investment

0 5 10 15 20 25 30

−0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 periods (years)

deviation from mean

0 5 10 15 20 25 30−0.03

−0.02 −0.01 0 0.01 0.02 0.03 0.04

deviation from mean

Aggregate profitability shock (left axis)

Investment rate (fixed ") (right axis)

Investment (empirical) (right axis)

0 5 10 15 20 25 30

−0.06 −0.03 0 0.03 0.06 0.09

periods (years)

deviation from mean

0 5 10 15 20 25 30−0.04

−0.02 0 0.02 0.04 0.06

deviation from mean

(62)

Aggregate Investment

0 5 10 15 20 25 30

−0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 periods (years)

deviation from mean

0 5 10 15 20 25 30−0.03

−0.02 −0.01 0 0.01 0.02 0.03 0.04

deviation from mean

Investment (Chat−Coop) (right axis)

0 5 10 15 20 25 30

−0.06 −0.03 0 0.03 0.06 0.09

periods (years)

deviation from mean

0 5 10 15 20 25 30−0.04

−0.02

0 0.02 0.04 0.06

deviation from mean

(63)

Aggregate Investment

0 5 10 15 20 25 30

−0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 periods (years)

deviation from mean

0 5 10 15 20 25 30−0.03

−0.02 −0.01 0 0.01 0.02 0.03 0.04

deviation from mean

Aggregate profitability shock (left axis) Investment rate (fixed ") (right axis)

0 5 10 15 20 25 30

−0.06 −0.03 0 0.03 0.06 0.09

periods (years)

deviation from mean

0 5 10 15 20 25 30−0.04

−0.02

0 0.02 0.04 0.06

deviation from mean

(64)

Aggregate Investment

0 5 10 15 20 25 30

−0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 periods (years)

deviation from mean

0 5 10 15 20 25 30−0.03

−0.02 −0.01 0 0.01 0.02 0.03 0.04

deviation from mean

Aggregate profitability shock (left axis) Investment rate (fixed ") (right axis) Investment (empirical) (right axis)

0 5 10 15 20 25 30

−0.06 −0.03 0 0.03 0.06 0.09

periods (years)

deviation from mean

0 5 10 15 20 25 30−0.04

−0.02 0 0.02 0.04 0.06

deviation from mean

(65)

Aggregate Investment

0 5 10 15 20 25 30

−0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04 periods (years)

deviation from mean

0 5 10 15 20 25 30−0.03

−0.02 −0.01 0 0.01 0.02 0.03 0.04

deviation from mean

Investment (Chat−Coop) (right axis)

0 5 10 15 20 25 30

−0.06 −0.03 0 0.03 0.06 0.09

periods (years)

deviation from mean

0 5 10 15 20 25 30−0.04

−0.02 0 0.02 0.04 0.06

deviation from mean

(66)

Correlation of aggregates with aggregate shock (A)

Extensive Margin Intensive Margin

Model ρA I K _KI Fraction of adjusters mean(Ii Ki|

Ii Ki>0.2)

Data 0.14 0.08 -0.02 0.12 0.14 NA

0.84 0.05 -0.36 0.23 0.19 NA

β 0.14 -0.51 0.03 -0.50 -0.55 0.61

0.84 0.55 0.73 0.43 0.46 0.09

˜

β(At,At+1) 0.14 0.61 0.15 0.58 0.62 0.01

(Empirical) 0.84 0.47 0.69 0.36 0.36 0.47

˜

β(At,At+1) 0.14 -0.19 0.10 -0.20 -0.23 0.49

(67)

Extensive margin

0 5 10 15 20 25 30 35 40 45 50

−0.04

−0.02 0 0.02 0.04

Extensive margin when ρ_A = 0.14

periods (years)

profitability shock

0 5 10 15 20 25 30 35 40 45 500.08

0.1 0.12 0.14 0.16

fraction of establishments with investment spike

Aggregate profitability shock (left axis) Spikes (empirical specification) Spikes (Chat−Coop specification)

0 5 10 15 20 25 30 35 40 45 50

−0.06

−0.03 0 0.03 0.06

periods (years)

profitability shock

0 5 10 15 20 25 30 35 40 45 500.08

0.1 0.12 0.14 0.16

(68)

Extensive margin

0 5 10 15 20 25 30 35 40 45 50

−0.04 −0.02 0 0.02 0.04

periods (years)

profitability shock

0 5 10 15 20 25 30 35 40 45 500.08

0.1 0.12 0.14 0.16

Aggregate profitability shock (left axis) Spikes (empirical specification) Spikes (Chat−Coop specification)

0 5 10 15 20 25 30 35 40 45 50

−0.06 −0.03 0 0.03 0.06

periods (years)

profitability shock

0 5 10 15 20 25 30 35 40 45 500.08

0.1 0.12 0.14 0.16

(69)

Aggregate capital regression:

K

t+1

=

K

(

A

t

,

K

t

)

Model ρA At Kt R2

Data 0.14 0.23 0.23 0.16

(0.08) (0.12)

0.84 0.13 0.98 0.90

(0.06) (0.05)

β 0.14 -0.33 0.71 0.64

(0.02) (0.03)

0.84 0.63 0.50 0.96

(0.02) (0.01) ˜

β(At,At+1) 0.14 0.60 0.58 0.72

(Empirical) (0.03) (0.02)

0.84 0.35 0.59 0.90

(0.02) (0.02) ˜

β(At,At+1) 0.14 -0.10 0.78 0.60

(Chat-Coop) (0.02) (0.03)

0.84 -0.09 0.74 0.66

(70)

Do Adjustment Costs Matter for Aggregate Investment in

Model with State-Dependent Discounting?

Table:Kt+1=K(At,Kt) from model using data-based SDDF (empirical)

Model ρA At Kt R2

Non-Convex AC 0.14 0.60 0.58 0.72

(0.03) (0.02)

0.84 0.35 0.59 0.90

(0.02) (0.02)

No AC 0.14 0.08 3.11 0.90

(0.01) (0.05)

0.84 0.18 1.20 0.91

(71)

Model with State-Dependent Discounting?

Model ρA At Kt R2

Non-Convex AC 0.14 0.60 0.58 0.72

(0.03) (0.02)

0.84 0.35 0.59 0.90

(0.02) (0.02)

No AC 0.14 0.08 3.11 0.90

(0.01) (0.05)

0.84 0.18 1.20 0.91

(72)

Model with State-Dependent Discounting?

Model ρA At Kt R2

Non-Convex AC 0.14 0.60 0.58 0.72

(0.03) (0.02)

0.84 0.35 0.59 0.90

(0.02) (0.02)

No AC 0.14 0.08 3.11 0.90

(0.01) (0.05)

0.84 0.18 1.20 0.91

(73)

Adjustment Costs Matter for Aggregate Investment in

Model with State-Dependent Discounting

Table:Kt+1=K(At,Kt) from model using model-based SDDF (Chat-Coop)

Model ρA At Kt R2

Non-Convex AC 0.14 -0.10 0.78 0.60

(0.02) (0.03)

0.84 -0.09 0.74 0.66

(0.01) (0.03)

No AC 0.14 0.40 1.03 0.68

(0.03) (0.04)

0.84 0.73 0.03 0.54

(74)

What have we learned?

Estimated ˜β process from data is qualitatively similar to model prediction, but small differences in the ˜β specification have large implications for investment behavior

Model-based SDDF contributes strongly to investment smoothing, data-based SDDF does not

Data on extensive margin of plant-level investment behavior show that model-based results overstate role of investment smoothing

Responsiveness of investment to aggregate shocks is affected by specification of aggregate shock process

(75)

What have we learned?

(76)

What have we learned?

(77)

What have we learned?

(78)

What have we learned?

(79)

Next steps

Study response of investment to monetary policy

How are changes in monetary policy reflected in changes in the

state-dependent discount factor?

Et h

˜

βt+1R j t+1

i

= 1

Specify a Taylor-type rule for the real interest rate

rtf =α+αAAt+αKKt+ρrtf−1+εft

(80)

Next steps

Study response of investment to monetary policy

How are changes in monetary policy reflected in changes in the

state-dependent discount factor?

Et h

˜

βt+1R j t+1

i

= 1

Specify a Taylor-type rule for the real interest rate

rtf =α+αAAt+αKKt+ρrtf−1+εft

(81)

Table: Parameter estimates for Solow-residual technology process

λ ρA σA

7 0.14 0.012

100 0.45 0.015

(82)

Differences from model-based predictions

Thomas (2002)

JOURNAL OF POLITICAL ECONOMY

TABLE 4

STANDARD DEVIATIONS RELATIVE TO OUTPUT

Output (1)

Investment

(2) Employment (3) Consumption (4) Wage (5) Interest

Rate (6)

Data 2.16 2.901 .959 .540 .287 .444

Benchmark 1.85 3.303 .577 .492 .492 .096

State-dependent

adjustment 1.85 3.304 .576 .492 .492 .095

Constant

adjustment 1.82 3.227 .556 .503 .503 .083

Partial adjustment 1.51 2.223 .305 .708 .708 .019

NOTE.-COI. 1 reports the percentage standard deviations for Hodrick-Prescott-filtered output in the data and the models. (Models are briefly summarized in table 3.) Cols. 2-6 are standard deviations relative to the standard deviation of output. In tables 4-7, the Hansen preference specification implies identical consumption and wage moments within each model economy.

what is perhaps more striking is that the inclusion of state-dependent lumpy investment patterns neither improves nor even affects model performance along any of these dimensions.

Table 4 reveals that the standard deviations for output, investment, employment, and consumption are essentially identical for the bench- mark and state-dependent adjustment economies. The similarities there extend to the constant adjustment model as well, which exhibits only somewhat reduced investment volatility. That closeness is further em- phasized by contrast to the traditional partial adjustment model, which exhibits a substantially weakened cycle because of excessively smooth investment demand. The overall similarity across models is also seen in the first- and second-order autocorrelations of table 6 and in the con- temporaneous and lagged correlations with output reported in tables 5 and 7. Consistent with its slightly reduced relative investment volatility, autocorrelations for the constant adjustment model's output, invest- ment, and employment series are somewhat higher, as are its investment and employment correlations with output.

The discussion above raises two questions. First, given that adjustment

TABLE 5

CONTEMPORANEOUS CORRELATIONS WITH OUTPUT

Investment

(1) Employment (2) Consumption (3) Wage

(4)

Interest Rate

(5)

Data .823 .903 .858 .263 -.385

Benchmark .973 .946 .924 .924 .889

State-dependent

adjustment .973 .946 .925 .925 .892

Constant adjustment .976 .950 .938 .938 .904

Partial adjustment .991 .971 .995 .995 .610

(83)

Differences from model-based predictions

Thomas (2002)

JOURNAL OF POLITICAL ECONOMY

TABLE 4

STANDARD DEVIATIONS RELATIVE TO OUTPUT

Output (1)

Investment

(2) Employment (3) Consumption (4) Wage (5) Interest

Rate (6)

Data 2.16 2.901 .959 .540 .287 .444

Benchmark 1.85 3.303 .577 .492 .492 .096

State-dependent

adjustment 1.85 3.304 .576 .492 .492 .095

Constant

adjustment 1.82 3.227 .556 .503 .503 .083

Partial adjustment 1.51 2.223 .305 .708 .708 .019

NOTE.-COI. 1 reports the percentage standard deviations for Hodrick-Prescott-filtered output in the data and the models. (Models are briefly summarized in table 3.) Cols. 2-6 are standard deviations relative to the standard deviation of output. In tables 4-7, the Hansen preference specification implies identical consumption and wage moments within each model economy.

what is perhaps more striking is that the inclusion of state-dependent lumpy investment patterns neither improves nor even affects model performance along any of these dimensions.

Table 4 reveals that the standard deviations for output, investment, employment, and consumption are essentially identical for the bench- mark and state-dependent adjustment economies. The similarities there extend to the constant adjustment model as well, which exhibits only somewhat reduced investment volatility. That closeness is further em- phasized by contrast to the traditional partial adjustment model, which exhibits a substantially weakened cycle because of excessively smooth investment demand. The overall similarity across models is also seen in the first- and second-order autocorrelations of table 6 and in the con- temporaneous and lagged correlations with output reported in tables 5 and 7. Consistent with its slightly reduced relative investment volatility, autocorrelations for the constant adjustment model's output, invest- ment, and employment series are somewhat higher, as are its investment and employment correlations with output.

The discussion above raises two questions. First, given that adjustment

TABLE 5

CONTEMPORANEOUS CORRELATIONS WITH OUTPUT

Investment

(1) Employment (2) Consumption (3) Wage (4)

Interest Rate

(5)

Data .823 .903 .858 .263 -.385

Benchmark .973 .946 .924 .924 .889

State-dependent

adjustment .973 .946 .925 .925 .892

Constant adjustment .976 .950 .938 .938 .904

Partial adjustment .991 .971 .995 .995 .610

(84)

Parameters:

From aggregate data (1948-2008)

ρA = 0.118 σA = 0.012

State-dependent discounting: ˆ

˜

βt+1 = 0.217ˆAt−0.507ˆAt+1

(85)

Parameters:

From aggregate data (1948-2008)

ρA = 0.118 σA = 0.012

State-dependent discounting: ˆ

˜

βt+1 = 0.217ˆAt−0.507ˆAt+1