Information, Misallocation and Aggregate Productivity Joel M. David USC

Hugo A. Hopenhayn

Venky Venkateswaran

UCLA

NYU Stern

Sep 2015

1 / 27

This paper “Misallocation,” i.e., dispersion in MP’s ⇒ large losses in TFP and output • But sources of distortions still unclear... • Role of imperfect information? Informational role of financial markets?

1. What we do • Heterogeneous firms choose inputs under imperfect info • Firms learn from internal sources and noisy asset prices • Quantify frictions using stock market/production data in US, China, India

2. What we find • Significant micro uncertainty, esp. in China and India

→ accounts for 20-50% (+...) of MRPK dispersion • Sizable aggregate impact

→ TFP losses: 7-10% in China and India, 4% in US; lower bound...? • Only limited learning from markets; firm internal sources are key 2 / 27

This paper “Misallocation,” i.e., dispersion in MP’s ⇒ large losses in TFP and output • But sources of distortions still unclear... • Role of imperfect information? Informational role of financial markets?

1. What we do • Heterogeneous firms choose inputs under imperfect info • Firms learn from internal sources and noisy asset prices • Quantify frictions using stock market/production data in US, China, India

2. What we find • Significant micro uncertainty, esp. in China and India

→ accounts for 20-50% (+...) of MRPK dispersion • Sizable aggregate impact

→ TFP losses: 7-10% in China and India, 4% in US; lower bound...? • Only limited learning from markets; firm internal sources are key 2 / 27

This paper “Misallocation,” i.e., dispersion in MP’s ⇒ large losses in TFP and output • But sources of distortions still unclear... • Role of imperfect information? Informational role of financial markets?

1. What we do • Heterogeneous firms choose inputs under imperfect info • Firms learn from internal sources and noisy asset prices • Quantify frictions using stock market/production data in US, China, India

2. What we find • Significant micro uncertainty, esp. in China and India

→ accounts for 20-50% (+...) of MRPK dispersion • Sizable aggregate impact

→ TFP losses: 7-10% in China and India, 4% in US; lower bound...? • Only limited learning from markets; firm internal sources are key 2 / 27

Overview

• Simplified model

• Full model and numerical results

• Robustness

• Other evidence

3 / 27

Simplified model Homogeneous good, only capital, no aggregate risk • Continuum of producers:

Yit = Ait Kitα ,

ait ∼ iid, N 0, σµ2




Input choice under incomplete info: • Profit maximization:

maxKit Eit [Ait ] Kitα − RKit

• Conditional on info Iit , ait ∼ N (Eit ait , V)

V is key object: • Misallocation: • Aggregate TFP :

2 σmpk =V

a = a∗ −

1 α σ2 2 1−α mpk

= a∗ −

1 α V 2 1−α

⇒ TFP ↓ in V; size of effect ↑ in α

4 / 27

Simplified model Homogeneous good, only capital, no aggregate risk • Continuum of producers:

Yit = Ait Kitα ,

ait ∼ iid, N 0, σµ2




Input choice under incomplete info: • Profit maximization:

maxKit Eit [Ait ] Kitα − RKit

• Conditional on info Iit , ait ∼ N (Eit ait , V)

V is key object: • Misallocation: • Aggregate TFP :

2 σmpk =V

a = a∗ −

1 α σ2 2 1−α mpk

= a∗ −

1 α V 2 1−α

⇒ TFP ↓ in V; size of effect ↑ in α

4 / 27

Simplified model Homogeneous good, only capital, no aggregate risk • Continuum of producers:

Yit = Ait Kitα ,

ait ∼ iid, N 0, σµ2




Input choice under incomplete info: • Profit maximization:

maxKit Eit [Ait ] Kitα − RKit

• Conditional on info Iit , ait ∼ N (Eit ait , V)

V is key object: • Misallocation: • Aggregate TFP :

2 σmpk =V

a = a∗ −

1 α σ2 2 1−α mpk

= a∗ −

1 α V 2 1−α

⇒ TFP ↓ in V; size of effect ↑ in α

4 / 27

Characterizing V

The firm’s information set Iit 1. Private signal: sit = ait + eit ,

eit ∼ N 0, σe2

pit ≈ ait + ηit ,

ηit ∼ N 0, ση2

2. Stock price:





If (ait , eit , ηit ) independent (relaxed later): V=

1 1 2 σµ

+

1 σe2

+

1 2 ση

5 / 27

Characterizing V

The firm’s information set Iit 1. Private signal: sit = ait + eit ,

eit ∼ N 0, σe2

pit ≈ ait + ηit ,

ηit ∼ N 0, ση2

2. Stock price:





If (ait , eit , ηit ) independent (relaxed later): V=

1 1 2 σµ

+

1 σe2

+

1 2 ση

5 / 27

Identifying information frictions The challenge: information Iit not directly observable kit =

Eit [ait ] 1−α

2 → In principle, could identify V from σmpk , σk2 , σak , etc...

But, suppose: kit =

Eit [ait + τit ] 1−α

→ Other ‘distortions’ complicate inference from these moments Our strategy: • Use correlation of stock returns with ∆kit and ∆ait (denoted ρpk , ρpa ) • Model implies tight connection between these correlations and V

6 / 27

Identifying information frictions The challenge: information Iit not directly observable kit =

Eit [ait ] 1−α

2 → In principle, could identify V from σmpk , σk2 , σak , etc...

But, suppose: kit =

Eit [ait + τit ] 1−α

→ Other ‘distortions’ complicate inference from these moments Our strategy: • Use correlation of stock returns with ∆kit and ∆ait (denoted ρpk , ρpa ) • Model implies tight connection between these correlations and V

6 / 27

Identifying information frictions The challenge: information Iit not directly observable kit =

Eit [ait ] 1−α

2 → In principle, could identify V from σmpk , σk2 , σak , etc...

But, suppose: kit =

Eit [ait + τit ] 1−α

→ Other ‘distortions’ complicate inference from these moments Our strategy: • Use correlation of stock returns with ∆kit and ∆ait (denoted ρpk , ρpa ) • Model implies tight connection between these correlations and V

6 / 27

Identifying information frictions The challenge: information Iit not directly observable kit =

Eit [ait ] 1−α

2 → In principle, could identify V from σmpk , σk2 , σak , etc...

But, suppose: kit =

Eit [ait + τit ] 1−α

→ Other ‘distortions’ complicate inference from these moments Our strategy: • Use correlation of stock returns with ∆kit and ∆ait (denoted ρpk , ρpa ) • Model implies tight connection between these correlations and V

6 / 27

Identification - our strategy

1. Directly measure ait = yit − αkit (and so, σµ2 )

1

ρpa = r 1+ ρpa

→

2 ση

V =1− σµ2



ρpa ρpk

2

2 σµ

noise in prices

ρpk relative to ρpa → firm uncertainty 3. Straightforward to add persistence. • E.g., with permanent shocks, ρpk − ρpa

→

V 2 σµ

Next: Robustness to other distortions τit , measurement error etc. 7 / 27

Identification - our strategy

1. Directly measure ait = yit − αkit (and so, σµ2 ) 2. For now, τit = 0.

1

ρpa = r 1+ ρpa

→

2 ση

V =1− σµ2



ρpa ρpk

2

2 σµ

noise in prices

ρpk relative to ρpa → firm uncertainty 3. Straightforward to add persistence. • E.g., with permanent shocks, ρpk − ρpa

→

V 2 σµ

Next: Robustness to other distortions τit , measurement error etc. 7 / 27

Identification - our strategy

1. Directly measure ait = yit − αkit (and so, σµ2 ) 2. For now, τit = 0.

1

ρpa = r 1+ ρpa

→

2 ση

V =1− σµ2



ρpa ρpk

2

2 σµ

noise in prices

ρpk relative to ρpa → firm uncertainty 3. Straightforward to add persistence. • E.g., with permanent shocks, ρpk − ρpa

→

V 2 σµ

Next: Robustness to other distortions τit , measurement error etc. 7 / 27

Identification - our strategy

1. Directly measure ait = yit − αkit (and so, σµ2 ) 2. For now, τit = 0.

1

ρpa = r 1+ ρpa

→

2 ση

V =1− σµ2



ρpa ρpk

2

2 σµ

noise in prices

ρpk relative to ρpa → firm uncertainty 3. Straightforward to add persistence. • E.g., with permanent shocks, ρpk − ρpa

→

V 2 σµ

Next: Robustness to other distortions τit , measurement error etc. 7 / 27

Identification - other frictions Distortions from correlated and uncorrelated factors (with ait ):   τit = γµit + εit , εit ∼ N 0, σε2 ⇒ kit =

(1 + γ) E [ait ] + εit 1−α

1. Only correlated distortions (γ 6= 0, σε2 = 0):  2 ρpa 2 ⇒ σmpk > V; but, 1 − ρpk = σV2 still holds µ

2. Only uncorrelated distortions (γ = 0, σε2 6= 0):  2 σ2 ρpa 2 = σV2 − σ2ε < σV2 (conservative) ⇒ σmpk > V; but, 1 − ρpk µ

µ

µ

Note: Results extend to permanent shocks as well

8 / 27

Identification - other frictions Distortions from correlated and uncorrelated factors (with ait ):   τit = γµit + εit , εit ∼ N 0, σε2 ⇒ kit =

(1 + γ) E [ait ] + εit 1−α

1. Only correlated distortions (γ 6= 0, σε2 = 0):  2 ρpa 2 ⇒ σmpk > V; but, 1 − ρpk = σV2 still holds µ

2. Only uncorrelated distortions (γ = 0, σε2 6= 0):  2 σ2 ρpa 2 = σV2 − σ2ε < σV2 (conservative) ⇒ σmpk > V; but, 1 − ρpk µ

µ

µ

Note: Results extend to permanent shocks as well

8 / 27

Identification - other frictions Distortions from correlated and uncorrelated factors (with ait ):   τit = γµit + εit , εit ∼ N 0, σε2 ⇒ kit =

(1 + γ) E [ait ] + εit 1−α

1. Only correlated distortions (γ 6= 0, σε2 = 0):  2 ρpa 2 ⇒ σmpk > V; but, 1 − ρpk = σV2 still holds µ

2. Only uncorrelated distortions (γ = 0, σε2 6= 0):  2 σ2 ρpa 2 = σV2 − σ2ε < σV2 (conservative) ⇒ σmpk > V; but, 1 − ρpk µ

µ

µ

Note: Results extend to permanent shocks as well

8 / 27

Identification - other frictions Distortions from correlated and uncorrelated factors (with ait ):   τit = γµit + εit , εit ∼ N 0, σε2 ⇒ kit =

(1 + γ) E [ait ] + εit 1−α

1. Only correlated distortions (γ 6= 0, σε2 = 0):  2 ρpa 2 ⇒ σmpk > V; but, 1 − ρpk = σV2 still holds µ

2. Only uncorrelated distortions (γ = 0, σε2 6= 0):  2 σ2 ρpa 2 = σV2 − σ2ε < σV2 (conservative) ⇒ σmpk > V; but, 1 − ρpk µ

µ

µ

Note: Results extend to permanent shocks as well

8 / 27

Identification - Robustness 1. Unaffected by correlation in firm/market information

3. Robust to heterogeneity in α: kit = • Correlated:

1−α 1−αi

Eit (ait ) 1−αi

∝ Eit (ait ) ⇒ kit =

=

1−α Eit (ait ) 1−αi 1−α

(1+γ)Eit (ait ) 1−α

• Uncorrelated: does not affect (ρpk , ρpa )

9 / 27

Identification - Robustness 1. Unaffected by correlation in firm/market information 2. Ambiguous effects from measurement error ρ2pa

• In yit :

1−

2 σµ 2 +σ 2 σµ y

!

1−

>

ρ2pk

ρ2pa ρ2pk

=

V 2 σµ

!

2 σµ 2 +α2 σ 2 σµ k ! 2 −V σµ 2 −V (1−α)2 σ 2 +σµ k

ρ2pa

• In kit : 1 − ρ2pk

> 1−

3. Robust to heterogeneity in α: kit = • Correlated:

1−α 1−αi

Eit (ait ) 1−αi

∝ Eit (ait ) ⇒ kit =

ρ2pa ρ2pk

=

=

V 2 σµ

iff

V 2 σµ

<

2α−1 α2

1−α Eit (ait ) 1−αi 1−α

(1+γ)Eit (ait ) 1−α

• Uncorrelated: does not affect (ρpk , ρpa )

9 / 27

Identification - Robustness 1. Unaffected by correlation in firm/market information 2. Ambiguous effects from measurement error ρ2pa

• In yit :

1−

2 σµ 2 +σ 2 σµ y

!

1−

>

ρ2pk

ρ2pa ρ2pk

=

V 2 σµ

!

2 σµ 2 +α2 σ 2 σµ k ! 2 −V σµ 2 −V (1−α)2 σ 2 +σµ k

ρ2pa

• In kit : 1 − ρ2pk

> 1−

3. Robust to heterogeneity in α: kit = • Correlated:

1−α 1−αi

Eit (ait ) 1−αi

∝ Eit (ait ) ⇒ kit =

ρ2pa ρ2pk

=

=

V 2 σµ

iff

V 2 σµ

<

2α−1 α2

1−α Eit (ait ) 1−αi 1−α

(1+γ)Eit (ait ) 1−α

• Uncorrelated: does not affect (ρpk , ρpa )

9 / 27

Quantitative analysis: Model

1. Monopolistic competition: Yt =

 R

θ−1 θ

Ait Yit



θ θ−1

di

2 2. Production: Yit = Kitα1 Lα it

• Case 1: both factors chosen under imperfect info • Case 2: only K chosen under imperfect info, L adjusts ex-post

⇒ Preserves maxKit ΠEit [Ait ] Kitα − RKit ; with αCase 1 > αCase 2 3. AR(1) process for log Ait :

ait = ρait−1 + µit ,

µit ∼ N 0, σµ2




4. Explicit model of stock market trading ⇒ Preserves pit ≈I ait + ηit

10 / 27

Quantitative analysis: Model

1. Monopolistic competition: Yt =

 R

θ−1 θ

Ait Yit



θ θ−1

di

2 2. Production: Yit = Kitα1 Lα it

• Case 1: both factors chosen under imperfect info • Case 2: only K chosen under imperfect info, L adjusts ex-post

⇒ Preserves maxKit ΠEit [Ait ] Kitα − RKit ; with αCase 1 > αCase 2 3. AR(1) process for log Ait :

ait = ρait−1 + µit ,

µit ∼ N 0, σµ2




4. Explicit model of stock market trading ⇒ Preserves pit ≈I ait + ηit

10 / 27

The stock market Unit measure of firm equity traded by 2 type of agents 1. Investors: can purchase up to single unit at price pit 2. Noise traders: purchase random quantity Φ (zit ) , zit ∼ N 0, σz2




Information of investors: • Private signal: sijt = ait + vijt , vijt ∼ N 0, σv2




• Stock price: pit

Trading: buy asset if Eijt Πit ≥ pit Market clearing:

or

sijt > sbit

  sbit − ait 1−Φ + Φ (zit ) = 1 σν | {z } | {z } Noise traders Investors

⇒ Info in price:

sbit = ait + σν zit



ση2 = σv2 σz2



11 / 27

The stock market Unit measure of firm equity traded by 2 type of agents 1. Investors: can purchase up to single unit at price pit 2. Noise traders: purchase random quantity Φ (zit ) , zit ∼ N 0, σz2




Information of investors: • Private signal: sijt = ait + vijt , vijt ∼ N 0, σv2




• Stock price: pit

Trading: buy asset if Eijt Πit ≥ pit Market clearing:

or

sijt > sbit

  sbit − ait 1−Φ + Φ (zit ) = 1 σν | {z } | {z } Noise traders Investors

⇒ Info in price:

sbit = ait + σν zit



ση2 = σv2 σz2



11 / 27

The stock market Unit measure of firm equity traded by 2 type of agents 1. Investors: can purchase up to single unit at price pit 2. Noise traders: purchase random quantity Φ (zit ) , zit ∼ N 0, σz2




Information of investors: • Private signal: sijt = ait + vijt , vijt ∼ N 0, σv2




• Stock price: pit

Trading: buy asset if Eijt Πit ≥ pit Market clearing:

or

sijt > sbit

  sbit − ait 1−Φ + Φ (zit ) = 1 σν | {z } | {z } Noise traders Investors

⇒ Info in price:

sbit = ait + σν zit



ση2 = σv2 σz2



11 / 27

The stock market Unit measure of firm equity traded by 2 type of agents 1. Investors: can purchase up to single unit at price pit 2. Noise traders: purchase random quantity Φ (zit ) , zit ∼ N 0, σz2




Information of investors: • Private signal: sijt = ait + vijt , vijt ∼ N 0, σv2




• Stock price: pit

Trading: buy asset if Eijt Πit ≥ pit Market clearing:

or

sijt > sbit

  sbit − ait 1−Φ + Φ (zit ) = 1 σν | {z } | {z } Noise traders Investors

⇒ Info in price:

sbit = ait + σν zit



ση2 = σv2 σz2



11 / 27

Parameterization: general parameters

Parameter

Description

Target/Value

Time period

3 years

β

Discount rate

0.90

α1

Capital share

0.33

α2

Labor share

0.67

θ

Elasticity of substitution

6

• If K and L both chosen under imperfect information (case 1)

→

α=

θ−1 θ

= 0.83

• If only K chosen under imperfect information (case 2)

→

α = 0.62

12 / 27

Parameterization: country-specific parameters

Parameter

Description

ρ

Persistence of fundamentals

σµ2

Shocks to fundamentals

σe2

Firm private info

σv2

Investor private info

σz2

Noise trading

Targets )

From observed ait = revit − αkit

    ρpi ρpa    σ2 p

13 / 27

Identifying info frictions - quantitative model

1.4 1.2

0.15

Noise in prices

Posterior variance, V

0.2

0.1

0.05

1 0.8 0.6 0.4 0.2

0

−0.1

0 0.1 Relative correlation

0.2

0 0.2

0.3

0.4 Corr(dp,da)

0.5

0.6

Size of noise trader shock

4.5 4 ⇒ Same intuition as in simplified version: 3.5 3

• ρpa → noise in prices 2.5 • (ρpi − ρpa ) → V

2 1.5 1 0.17

0.18

0.19 0.2 0.21 Volatility of returns

0.22

14 / 27

The impact of informational frictions

V 2 σµ

V 2 σmrpk

a∗ − a

US

0.41

0.22

0.04

China

0.63

0.34

0.07

India

0.77

0.48

0.10

US

0.63

0.35

0.40

China

0.65

0.39

0.55

India

0.86

0.56

0.77

Case 2 (α = 0.62)

Case 1 (α = 0.83)

• Substantial posterior uncertainty (US firms best informed)

⇒ significant misallocation, losses in TFP and output • Effects increase with α 15 / 27

Discussion

1. Case 1 vs. Case 2 • Interpret our results as bounds; but can we say something more...? • Suggestive statistics from the US data •

2 σmrpl

= 0.57

2 σmrpk V • 2 computed σµ

with Nit ≈ 0.5 σV2 computed with Kit µ

2. Transitory vs. permanent MRPK deviations • Informational frictions → transitory deviations • US data: transitory ≈ 1/3 of total • V accounts for 60% in case 2; entirety in case 1

16 / 27

Discussion

1. Case 1 vs. Case 2 • Interpret our results as bounds; but can we say something more...? • Suggestive statistics from the US data •

2 σmrpl

= 0.57

2 σmrpk V • 2 computed σµ

with Nit ≈ 0.5 σV2 computed with Kit µ

2. Transitory vs. permanent MRPK deviations • Informational frictions → transitory deviations • US data: transitory ≈ 1/3 of total • V accounts for 60% in case 2; entirety in case 1

16 / 27

Sources of learning

Share from source ∆a

Private

Market

Case 2 US China India

5% 4% 3%

92% 96% 89%

8% 4% 11%

Case 1 US China India

23% 30% 12%

91% 96% 96%

9% 4% 4%

1. Significant learning ⇒ significant aggregate gains 2. Learning primarily from private sources Interpretation? Manager skill/incentives, info collection/processing, etc... 3. Only small role for market-generated info ⇐ just too much noise in prices 17 / 27

Effect of US information structure

Case 2

Case 1

∆a

∆a

Market Information China India

1% 1%

2% 4%

Private Information China India

3% 5%

6% 26%

Shocks China India

1% 2%

10% 20%

1. Gains from US private info > US market info 2. Differences in fundamentals → differential impact of friction

18 / 27

Robustness: correlated information

Are we picking up correlation between firm and investors’ signals ? • Correlated errors → ↑ ρpk →↑ V? • Strategy: Re-estimate V assuming sijt = sit + vijt V 2 σµ

V 2 σµ

= ait + eit + vijt

baseline

a∗ − a

a∗ − a baseline

Case 2 (α = 0.62) US

0.41

0.41

0.040

0.040

China

0.58

0.63

0.070

0.075

India

0.68

0.77

0.100

0.114

⇒ Results almost identical to baseline !

19 / 27

Robustness: correlated information

Are we picking up correlation between firm and investors’ signals ? • Correlated errors → ↑ ρpk →↑ V? • Strategy: Re-estimate V assuming sijt = sit + vijt V 2 σµ

V 2 σµ

= ait + eit + vijt

baseline

a∗ − a

a∗ − a baseline

Case 2 (α = 0.62) US

0.41

0.41

0.040

0.040

China

0.58

0.63

0.070

0.075

India

0.68

0.77

0.100

0.114

⇒ Results almost identical to baseline !

19 / 27

Robustness: measurement error in revenues What if observed

yˆit = yit + yit

2 yit ∼ N(0, σy )?

2 • σy → ↓ ρpa →↑ V

• Strategy: Re-estimate V with corrected moments

Baseline

2 = 10% σ 2 (∆y ) σy

2 = 25% σ 2 (∆y ) σy

V

V 2 σµ

V

V 2 σµ

V

V 2 σµ

Case 2 US China India

0.08 0.16 0.22

0.41 0.63 0.77

0.05 0.14 0.17

0.28 0.58 0.65

0.01 0.10 0.14

0.07 0.51 0.61

Case 1 US China India

0.13 0.18 0.26

0.63 0.65 0.86

0.12 0.18 0.25

0.62 0.69 0.91

0.07 0.17 0.22

0.42 0.73 0.89

⇒ Upward bias in V, but cross-country results biased downward. 20 / 27

Robustness: measurement error in revenues What if observed

yˆit = yit + yit

2 yit ∼ N(0, σy )?

2 • σy → ↓ ρpa →↑ V

• Strategy: Re-estimate V with corrected moments

Baseline

2 = 10% σ 2 (∆y ) σy

2 = 25% σ 2 (∆y ) σy

V

V 2 σµ

V

V 2 σµ

V

V 2 σµ

Case 2 US China India

0.08 0.16 0.22

0.41 0.63 0.77

0.05 0.14 0.17

0.28 0.58 0.65

0.01 0.10 0.14

0.07 0.51 0.61

Case 1 US China India

0.13 0.18 0.26

0.63 0.65 0.86

0.12 0.18 0.25

0.62 0.69 0.91

0.07 0.17 0.22

0.42 0.73 0.89

⇒ Upward bias in V, but cross-country results biased downward. 20 / 27

Robustness: measurement error in capital What if observed

kˆit = kit + kit

2 kit ∼ N(0, σk )?

2 • σk → ↓ ρpa , ρpk → V ?

• Strategy: Re-estimate V with corrected moments Baseline

2 = 10% σ 2 (∆y ) σk

V

V 2 σµ

V

V 2 σµ

Case 2 US China India

0.08 0.16 0.22

0.41 0.63 0.77

0.11 0.17 0.22

0.59 0.69 0.79

Case 1 US China India

0.13 0.18 0.26

0.63 0.65 0.86

0.17 0.21 0.27

0.85 0.79 0.95

⇒ Our approach underestimates uncertainty ! 21 / 27

Robustness: measurement error in capital What if observed

kˆit = kit + kit

2 kit ∼ N(0, σk )?

2 • σk → ↓ ρpa , ρpk → V ?

• Strategy: Re-estimate V with corrected moments Baseline

2 = 10% σ 2 (∆y ) σk

V

V 2 σµ

V

V 2 σµ

Case 2 US China India

0.08 0.16 0.22

0.41 0.63 0.77

0.11 0.17 0.22

0.59 0.69 0.79

Case 1 US China India

0.13 0.18 0.26

0.63 0.65 0.86

0.17 0.21 0.27

0.85 0.79 0.95

⇒ Our approach underestimates uncertainty ! 21 / 27

Robustness: adjustment costs

Are we re-labeling adjustment costs as info frictions ? • Strategy: Simulate moments under full-info and quadratic adj. costs • Estimate V using these moments

Adj. Cost V

Baseline V

US

0.03

0.08

China

0.06

0.16

India

0.08

0.22

• V (and agg effects) about 1/3 of baseline estimates

⇒ Unlikely that adj. costs are driving our estimates

22 / 27

Robustness: adjustment costs

Are we re-labeling adjustment costs as info frictions ? • Strategy: Simulate moments under full-info and quadratic adj. costs • Estimate V using these moments

Adj. Cost V

Baseline V

US

0.03

0.08

China

0.06

0.16

India

0.08

0.22

• V (and agg effects) about 1/3 of baseline estimates

⇒ Unlikely that adj. costs are driving our estimates

22 / 27

Robustness: financial frictions

Are we picking up financing-related effects of stock prices ? • Stock prices ↑ → Funding constraints ↓ → ρpk ↑ → V ↑? • Strategy: Estimate V for ‘unconstrained’ firms Baseline

US China India

Small Issuers

ρpi

ρpa

V 2 σµ

0.23 0.16 0.25

0.18 0.06 0.08

0.41 0.63 0.77

ρpi 0.15 0.18 0.20

Top Quartile

ρpa

V 2 σµ

ρpi

ρpa

V 2 σµ

0.06 0.06 0.08

0.58 0.60 0.62

0.19 0.24 0.25

0.14 0.05 0.07

0.46 0.76 0.93

⇒ Unlikely that the financing channel is driving our results

23 / 27

Robustness: financial frictions

Are we picking up financing-related effects of stock prices ? • Stock prices ↑ → Funding constraints ↓ → ρpk ↑ → V ↑? • Strategy: Estimate V for ‘unconstrained’ firms Baseline

US China India

Small Issuers

ρpi

ρpa

V 2 σµ

0.23 0.16 0.25

0.18 0.06 0.08

0.41 0.63 0.77

ρpi 0.15 0.18 0.20

Top Quartile

ρpa

V 2 σµ

ρpi

ρpa

V 2 σµ

0.06 0.06 0.08

0.58 0.60 0.62

0.19 0.24 0.25

0.14 0.05 0.07

0.46 0.76 0.93

⇒ Unlikely that the financing channel is driving our results

23 / 27

Other evidence: Cross-section • Compute V by sector in the US • Compare to mean squared error in firm revenue forecasts

24 / 27

Other evidence: Cross-section • Compute V by sector in the US • Compare to mean squared error in firm revenue forecasts

0.09

Trans. & PU

0.08 Mfg.

0.07 0.06

Const.

V

0.05 FIRE

Services

0.04 0.03 Ret. Trade 0.02 Whl. Trade

0.01 0 0

0.002

0.004

0.006 0.008 0.01 Forecast Dispersion

0.012

0.014

0.016

24 / 27

Other evidence: Time series • Compute V over time in the US • Compare to other indicators of micro uncertainty

25 / 27

Other evidence: Time series • Compute V over time in the US • Compare to other indicators of micro uncertainty

Deviations from Trend

2

1

0

−1 V Jurado et. al. −2 1998

2000

2002

2004

2006

2008

2010

2012

Year

Source: Jurado, Ludvigson and Ng, ”Measuring Uncertainty”, AER

25 / 27

Related literature Misallocation • Hsieh and Klenow (09), Restuccia and Rogerson (08), Bartelsman et.

al.(13)... • Financial frictions: Buera, Kaboski and Shin (11), Midrigan and Xu (13),... • Adjustment costs: Asker, Collard-Wexler and De Loecker (13) • Information frictions: Jovanovic (13)

Stock price informativeness • Morck, Yeung and Yu (00), Durnev, Yeung and Zarowin (03),...

The “feedback” effect (Bond, Edmans and Goldstein (12)) • Investment: Chen, Goldstein and Jiang (07), Bakke and Whited (10),

Morck, Schleifer and Vishny (90) • R&D spending: Bai, Philippon and Savov (13) • Mergers and acquisitions: Luo (05) 26 / 27

Conclusion

Theory linking micro uncertainty to misallocation and aggregates • Substantial uncertainty and associated aggregate losses • Limited informational role for stock markets • Significant role for private learning ⇒ drives cross-country differences

Where next? • Entry/exit • Other frictions...

27 / 27

Full-info TFP Simplified model: a∗ = General model: a∗ = simple model

general model

1 2



1 σµ2 21−α

θ θ−1



σa2 1−α

Identification with iid shocks

ρpa = r

1 1+

(& in σv σz ) σv2 σz2 2 σµ

ρpk = r 1+ σp2 =



1−β 1−α

1 

σv2 σz2 2 σµ

2

1−

V 2 σµ

2 2 σ + 1  z  1 σµ2 1 2 ρ2pa σ z + ρ2

(% in V)



pa

ident



(% in σz )

Identification with permanent shocks

V ρpk − ρpa 1 σµ = where η = σµ2 η 1 − α σp
1 − η2 η σv2 σz2 + = −1 σµ2 ρpa 2ρ2pa σz2 + 1 σz2 ident

+1+

σv2 σz2 2 σµ

=

1 η

Step 1. cov (p, k) = cov (p, a). • follows from k = E (a|p, si ) • and since we can write a = E (a|p, si ) + ε • cov (a, p) = cov (E (a|p, si ) , p) + cov (ε, p) = cov (k, p) .

Step 2. divide both sides by σa σp so we get [cov (p, k)]2 = ρ (p, a)2 (σa σp )2

(1)

Step 3. By the law of total covariance, σa2 = σk2 + V so σk2 V =1− 2 σa2 σa Substituting (2) in (1) we get   2  ρ (p, a) V 1− 2 = ρ (p, k) σa identical to our identification equation.

ident

(2)

Investment-Q regressions Reduced-form representation (with iid shocks): ∆kit = λ1 (∆µit + ∆eit ) + λ2 ∆pit Use model to derive: λ2 ∝

(1 + γ)V ση2

Intuition: λ2 could be large because of • high uncertainty (high V ) OR • more information prices (low ση2 ) OR • correlated distortions (high γ)

Also, consistency of λ2 requires ∆eit ⊥ ∆µit , ∆pit • Correlated signals → ∆eit correlated with ∆pit → endogeneity ident

Data and parameter values

Target moments

Parameters

ρpi

ρpa

σp2

Case 2 US China India

0.23 0.16 0.25

0.18 0.06 0.08

0.23 0.14 0.23

0.92 0.78 0.93

0.45 0.51 0.53

0.39 0.67 1.04

0.37 0.74 0.69

3.50 4.24 4.36

Case 1 US China India

0.24 0.15 0.26

0.10 0.02 0.00

0.23 0.14 0.22

0.88 0.75 0.88

0.46 0.53 0.55

0.63 0.74 1.39

0.65 1.18 1.69

3.16 3.14 4.14

ρ

σµ

σe

σv

σz

Data source: Compustat NA and Compustat Global.

• Cross-country variation in moments ⇒ variation in parameters • US: less fundamental uncertainty, better private info, less noise in markets results

Full-information adjustment cost model • Value function

    V A˜it , Kit−1 = max G A˜it Kitα˜ − Iit − H (Iit , Kit−1 ) + βEV A˜it+1 , Kit Kit ,Nit

where Iit = Kit − (1 − δ) Kit−1

and

H (Iit , Kit−1 ) = ζKit−1

˜it , Kit in GE • Solve numerically for joint distribution of A • Target ρpa , σp2 , σk2 to estimate (σv2 , σz2 , ζ)




• Simulate data to compute ρpi Back



Iit Kit−1

2