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
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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
