Misallocation or Mismeasurement? Mark Bils, University of Rochester - - PowerPoint PPT Presentation

Misallocation or Mismeasurement?

Mark Bils, University of Rochester and NBER Pete Klenow, Stanford University and NBER Cian Ruane, International Monetary Fund

January 2020

Any opinions and conclusions expressed herein are those of the author(s) and do not necessarily represent the views of the U.S. Census Bureau. This research was performed at a Federal Statistical Research Data Center under FSRDC Project 1440. All results have been reviewed to ensure that no confidential information is disclosed. The views expressed in this paper are those of the authors and should not be attributed to the International Monetary Fund, its Executive Board, or its management.

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Motivation

Widespread perception that resource misallocation an important cause of low aggregate productivity (TFP) in EMDEs Motivates structural reforms as a source of growth / convergence Gains from resource reallocation are difficult to quantify, but gains are potentially huge

◮ Banerjee & Duflo (2005) ◮ Restuccia & Rogerson (2008) ◮ Hsieh & Klenow (2009, 2014) ◮ Baqaee & Farhi (2019)

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Hsieh and Klenow (2009)

Large dispersion in revenue/inputs (TFPR) across plants in India, China and U.S. Interpret dispersion in TFPR as dispersion in marginal products ⇒ quantify misallocation Reducing resource misallocation in India and China to U.S. levels ⇒ increase TFP by 40% and 50% But dispersion in measured average products need not reflect dispersion in true marginal products

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U.S. manufacturing in recent decades

Kehrig (2015) noticed rising TFPR dispersion

◮ Suggests falling allocative efficiency

For 1978–2013 we find it would imply:

◮ A drag on TFP growth of 1.7 percentage points per year ◮ 45 percent lower TFP (cumulatively by 2013)

Has misallocation really increased dramatically? Or has mismeasurement and/or misspecification worsened?

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U.S. allocative efficiency

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What we do

Propose a way to estimate misallocation allowing for:

◮ Measurement error in revenue and inputs ◮ Misspecification due to overhead costs

Apply to:

◮ manufacturing plants in the U.S. 1978–2013 ◮ manufacturing plants in India 1985–2013

Preview of results:

◮ No longer a severe decline in U.S. allocative efficiency ◮ For U.S. potential gains ∼ 49% rather than ∼ 123% ◮ For India, potential gains ∼ 89% rather than ∼ 111%

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U.S. vs India corrected allocative efficiency

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Others skeptical of misallocation

Adjustment costs

◮ Asker, Collard-Wexler and De Loecker (2014) ◮ Kehrig and Vincent (2019)

Overhead costs

◮ Bartelsman, Haltiwanger and Scarpetta (2013)

Variable production elasticities

◮ David and Venkateswaran (2019)

Measurement error and imputation

◮ Rotemberg and White (2019)

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Outline

1

Illustrative example

2

Full model

3

TFPR dispersion in U.S. and Indian data

4

Estimating measurement and specification error

5

Corrected measures of misallocation

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Simple model setup

Y =

• i Y

1− 1

ǫ

i

• 1

1− 1 ǫ , P =

• i P 1−ǫ

i

• 1

1−ǫ

Yi = Ai · Li max

• 1 − τ Y

i

• PiYi − wLi

◮ Monopolistic competitor takes w, Y , and P as given

• PiYi = PiYi + gi
• Li = Li + fi

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Simple model TFPR

Pi =

• ǫ

ǫ − 1

• ×
• τi · w

Ai

• , where τi ≡

1 1 − τ Y

i

PiYi Li ∝ τi TFPRi ≡

• PiYi
• Li

∝ τi ·

• PiYi

PiYi · Li

• Li

Let ∆Xt ≡ Xt − Xt−1 Xt−1 for variable X

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Identifying misallocation vs. dispersion in TFPR

∆ PY i = ∆ Li · τi TFPRi

◮ assuming distortions and measurement error are fixed over time ◮ in which case ∆PiYi = ∆Li = (ǫ − 1) ∆Ai

We will generalize to allow:

◮ Sales R and a composite input I ◮ Shocks to distortions and to measurement errors

And regress ∆ R on ∆ I in different deciles of TFPR

◮ Measurement error should make coefficients fall with TFPR ◮ Will use this to estimate E (ln τi | ln TFPRi) ◮ Validate approach using simulations

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Outline

1

Illustrative example

2

Full model

3

TFPR dispersion in U.S. and Indian data

4

Identifying measurement and specification error

5

Corrected misallocation

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Full Model (Setup)

Closed economy, S sectors, Ns firms, L workers, K capital Q = S

s=1 Q θs s ,

Qs = Ns

i

Q

1− 1

ǫ

si

• 1

1− 1 ǫ

Qsi = Asi(Kαs

si L1−αs si

)γsX1−γs

si

max Rsi − (1 + τ L

si)wLsi − (1 + τ K si )rKsi − (1 + τ X si )Xsi

◮ Rsi ≡ PsiQsi ◮ Monopolistic competitor takes input prices as given

C = Q − X, X = S

s

Ns

i

Xsi

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Model (Aggregate TFP)

TFP ≡ C L1−

αK α

◮ where

α ≡ S

s=1 αsγsθs

S

s=1 γsθs

TFP = T ×

S

• s=1

TFP

θs S s=1 γsθs

s

◮ TFPs ≡

Qs (Kαs

s L1−αs s

)γsX1−γs

s

◮ T = reflects sectoral distortions (set aside)

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Model (Sectoral TFP)

Suppressing s here and whenever possible: TFP = N

• i

Aǫ−1

i

τi τ 1−ǫ

• 1

ǫ−1

τi ≡

• 1 + τ L

i

1−α 1 + τ K

i

αγ 1 + τ X

i

1−γ τ ≡

• 1 + τ L1−α

1 + τ Kαγ 1 + τ X1−γ where 1 + τ L ≡ N

i=1 Ri R 1 1+τ L

i

−1 and so on

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Model (Sectoral TFP Decomposition)

TFP = AE · PD · A · N

1 ǫ−1

AE ≡ Allocative Efficiency PD ≡ Productivity Dispersion A ≡ Average productivity N

1 ǫ−1 ≡ Variety

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Model (Sectoral TFP Decomposition)

TFP =

• 1

N

N

• i

Ai

• A

ǫ−1 τi τ 1−ǫ

• 1

ǫ−1

• AE=Allocative Efficiency

×

• 1

N

N

• i

Ai A ǫ−1

1 ǫ−1

• PD=Productivity Dispersion

× N

1 ǫ−1

Variety

× A

• Average Productivity
• A =
• 1

N

N

i (Ai)ǫ−1

1 ǫ−1

(power mean) A = N

i=1 A

1 N

i

(geometric mean)

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Full Model (Sectoral TFP Decomposition)

TFP ≡ Q (L1−αKα)γX1−γ =

• 1

N

N

• i

Ai

• A

ǫ−1 τi τ 1−ǫ

• 1

ǫ−1

• AE=Allocative Efficiency

× N

• i

(Ai)ǫ−1

• 1

ǫ−1

• Residual Productivity

τi ≡

• 1 + τ L

i

1−α 1 + τ K

i

αγ 1 + τ X

i

1−γ

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Aside: Intuition in a special case

If Ai and τi are jointly lognormal and τ L

i = τ K i

= τ X

i

then AE = ǫ 2 · Var [ln(τi)]

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Outline

1

Illustrative example

2

Full model

3

TFPR dispersion in U.S. and Indian data

4

Identifying measurement and specification error

5

Corrected misallocation

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Indian Annual Survey of Industries (ASI)

Survey of Indian manufacturing plants

◮ Long panel 1985–2013 ◮ Used in Hsieh and Klenow (2009, 2014)

Sampling frame

◮ All plants > 100 or 200 workers (45% of plant-years) ◮ Probabilistic if > 10 or 20 workers (55% of plant-years) ◮ ≈ 43,000 plants per year

Variables used

◮ Gross output (Ri), intermediate inputs (Xi), labor (Li), wage bill

(wLi), and capital (Ki)

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U.S. Longitudinal Research Database (LRD)

U.S. Census Bureau data on manufacturing plants

◮ Long panel, 1978–2013 ◮ Used in Hsieh and Klenow (2009, 2014)

Sampling frame

◮ Annual Survey of Manufacturing (ASM) plants ◮ ∼ 50k plants per year with at least one employee ◮ Quinquennial sample for ∼ 34k plants, certainty for other ∼ 16k

Variables used

◮ Gross output (Ri), intermediate inputs (Xi), labor (Li), wage bill

(wLi), and capital (Ki)

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Data cleaning steps

Step Cleaning 1 Starting sample of plant-years 2 Missing no key variables 3 Common sector concordance 4 Trim 1% of each left and right TFPR and TFPQ tail

1,806,000 plant-years for U.S. LRD 943,186 plant-years for Indian ASI

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Inferring allocative efficiency a la Hsieh & Klenow (2009)

AE = N

• i

TFPQi TFPQ ǫ−1 TFPRi TFPR 1−ǫ

1 ǫ−1

Ai = TFPQi = (Ri)

ǫ ǫ−1

(Kα

i L1−α i

)γX1−γ

i

TFPRi = Ri (Kα

i L1−α i

)γX1−γ

i 25 / 65

Inferring allocative efficiency as in Hsieh & Klenow (2009)

AE = N

• i

TFPQi TFPQ ǫ−1 TFPRi TFPR 1−ǫ

1 ǫ−1

TFPQ = N

i TFPQǫ−1 i

• 1

ǫ−1

TFPR =

• ǫ

ǫ−1 MRPL (1−α)γ

(1−α)γ

MRPK αγ

αγ

MRPX 1−γ

1−γ

◮ MRPK =

• i

Ri R 1 MRPKi −1 and so on

◮ MRPKi =

ǫ − 1 ǫ

• αγ Ri

Ki and so on

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Inferring aggregate AE

Aggregating within-sector allocative efficiencies: AEt =

S

• s=1

AE

θst S s=1 γsθst

st

Parameterization: ǫ = 4 based on Redding and Weinstein (2016) αs and γs inferred from sectoral cost-shares (r = .2) θst inferred from sectoral shares of aggregate output

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Indian allocative efficiency

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U.S. allocative efficiency

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Allocative efficiency in the U.S. relative to India

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TFPR Dispersion in the U.S. and India over time

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TFPQ Dispersion in the U.S. and India over time

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Elasticity of TFPR wrt TFPQ in the U.S and India

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Outline

1

Illustrative example

2

Full model

3

TFPR dispersion in U.S. and Indian data

4

Identifying measurement and specification error

5

Corrected misallocation

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Measurement error and ∆TFPR

Recall TFPRi = τi ·

• Ri

Ri · Ii

• Ii

∆TFPRi = ∆τi + ∆ Ri Ri

• − ∆

Ii Ii

• ∆ is the growth rate of a variable relative to the sector s mean.

Increases in Ri and Ii reduce the role of additive measurement error But have no impact on the role of multiplicative measurement error

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Previewing our empirical specification

We will regress revenue growth on input growth for a panel of plants: ∆ Ri = λk + βk ∆ Ii + ei i denotes plant k denotes one of K bins of TFPR ∆ is the growth rate of a variable relative to the sector s mean. Additive measurement error shows up as lower βk at higher TFPR’s

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Measurement error: key assumptions

Only additive measurement error

• Ii = Ii + fi;
• Ri = Ri + gi

◮ Conservative, as multiplicative also overstates TFPR differences ◮ Analogous to heterogeneous overhead costs

Common measurement error across inputs Zero covariance between ln (τi) and ln Ri Ri · Ii

• Ii
• 37 / 65

Look at elasticity of revenue wrt inputs

Define βk ≡ Covk

• ∆

R, ∆ I

• V ark
• ∆

I

• k indexes the level of TFPR (plant index i implicit)

βk is the population projection of ∆ R on ∆ I, at k–level TFPR

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βk in the absence of measurement error

If f = 0 and g = 0, then: ∆ I = ∆I = (ǫ − 1) ∆A − ǫ∆τ ∆ R = ∆R = (ǫ − 1)

• ∆A − ∆τ
• βk = 1 + φk

where φk ≡ Covk (∆τ, ∆I) V ark (∆I) = −ǫV ark (∆τ) + (ǫ − 1)Covk (∆τ, ∆A) V ark (∆I)

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βk in the absence of measurement error cont.

βk = 1 + φk φk = elasticity of ∆τ wrt ∆I If ∆τ is i.i.d., then does not project on TFPR

◮ ⇒ φk = φ ◮ ⇒

βk = β

If τ is stationary, then V ark (∆τ) larger at both high and low values of ln(TFPR) = ln(τ), so smaller βk at TFPR extremes

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βk in the presence of measurement error

βk ≈ Ek

• R

I

• RI
• (1 + φk) + ψk

≈ reflects for “small” changes: ∆A, ∆τ, d f

• I

, dg

• R

Recall TFPR = τ ·

• R

R · I

• I

Ek

• R

I

• RI
• captures role of both measurement errors in TFPR

Ek (τ) = Ek

• R

I

• RI
• · TFPRk

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Measurement error in revenue and inputs, cont.

Now φk reflects elasticities of ∆τ and d

f

• I wrt ∆

I φk ≡ Covk

• I
• I ∆τ − f′−f
• I

, ∆ I

• V ark
• ∆

I

• Added term ψk

ψk = 1 V ark

• ∆

I

• Covk

R I

• RI

, ∆ I

• ∆

I + I

• I

∆τ − f′ − f

• I
• −

Ek

• ∆

I

• Covk

R I

• RI

,

• ∆

I + I

• I

∆τ − f′ − f

• I
• + Covk

g′ − g

• R

, ∆ I

• 42 / 65

Recovering Ek (τ)

Ek (τ) = Ek

• R

I

• RI
• · TFPRk =

βk − ψk 1 + φk

• · TFPRk

If ∆τ, ∆A, d f

• I

and dg

• R

are i.i.d. = ⇒ ψk = 0, φk = φ Ek (τ) ∝ βk · TFPRk Model simulations to correct for large shocks and φk, ψk

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Getting dispersion in τ

Ek (τ) ∝ βk · TFPRk is τ dispersion that projects on TFPR With measurement error, also τ dispersion ⊥ to TFPR “Add back” dispersion, call term ε, in ln τ

◮ ε ⊥ ln TFPR ◮ ε ∼ N(0, σ2) ◮ σ2 chosen to hit var[ln(τ)] assuming ln

• R

I

• R I
• ⊥ ln τ

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Dispersion in τ, continued

ln TFPR = ln τ − ln

• R

I

• R I
• V ar
• ln τ
• =

V ar

• ln TFPR
• − V ar
• ln
• R

I

• RI
• + 2Cov
• ln τ, ln
• R

I

• RI
• Assuming Cov
• ln τ, ln
• R

I

• RI
• = 0

◮ Eliminates last term in V ar

• ln τ
• ◮ −V ar
• ln
• R

I

• R I
• = Cov
• ln TFPRk, Ek
• ln
• R

I

• R I
• 45 / 65

Dispersion in τ, continued

As a result: V ar

• ln τ
• =

V ar

• ln TFPR
• + Cov
• ln TFPRk, Ek
• ln
• R

I

• R I
• ◮ First term is data

◮ Second reflects how our βk estimates covary with TFPR

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TFPR correction implementation

Regress revenue growth on input growth by decile of TFPR:

◮ Divide 25+ year samples into 5/6-year windows ◮ Unbalanced panel of Indian and U.S. plants ◮ ≈ 28,000 / 6,000 plants per decile-window in U.S. / India

∆ Ri = λk + βk ∆ Ii + ei i denotes plant, k denotes decile

◮ ∆

Ri, ∆ Ii and TFPR are deviations from sector-year average

◮ Use Tornqvist average of TFPR for constructing deciles ◮ Regressions are cost-share weighted ◮ Trim observations where TFPR changes by factor > 5

Merge βk estimates into non-panel sample by decile-window: ln ( τi) = ln(TFPRi) + ln( βk) + εi

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• βk’s wrt TFPRk, India and U.S.

Table: Coefficients βk for revenue growth on input growth by TFPR decile

k → 1 2 3 4 5 6 7 8 9 10 India 1.09 1.04 1.03 1.00 1.01 0.99 1.00 0.99 0.95 0.88 U.S. 1.05 1.00 0.97 0.96 0.93 0.90 0.86 0.84 0.70 0.54

Source: Indian ASI 1985–2013 and U.S. LRD 1978–2013. TFPR deciles are constructed as Tornqvist deviations from the (cost-weighted) sector-year average. Regressions weight by plant’s input costs. Standard errors are clustered at the industry level, and are uniformly below 0.02. 48 / 65

Indian βk slopes wrt TFPRk

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U.S. βk slopes wrt TFPRk

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• τ dispersion vs. TFPR dispersion

India

1985–1991 1992–1996 1997–2001 2002–2007 2008–2013 σ2

• τ/σ2

T F P R

0.68 0.76 0.74 0.69 0.71

U.S.

1978–1984 1985–1991 1992–1998 1999–2005 2006–2013 σ2

• τ/σ2

T F P R

0.40 0.43 0.38 0.32 0.28

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Allocative efficiency in India

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Allocative efficiency in the U.S.

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Uncorrected vs. corrected gains from reallocation

INDIA 1985–2013

Mean S.D. Uncorrected gains 110.9% 17.3% Corrected gains (estimates) 87.8% 13.8% Shrinkage 21% 20%

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Uncorrected vs. corrected gains from reallocation

U.S. 1978–2013

Mean S.D. Uncorrected gains 123.2% 59.7% Corrected gains (estimates) 49.1% 12.2% Shrinkage 60% 80%

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Cumulative change in AE

U.S. INDIA 1978–2013 1985–2013 Uncorrected

• 45%
• 1.5%

Corrected

• 16%
• 0.8%

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Allocative efficiency: U.S. relative to India

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Dispersion of U.S. TFPR

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Elasticity of TFPR wrt TFPQ in the U.S.

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Dispersion of TFPQ in the U.S.

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Simulations to test the validity of our strategy

Ait = Ai · ait where ln(Ai) ∼ N(0, σ2

A)

ait and τit follow ln(xit) = ρx · ln(xit−1) + ηx

it where ηx it ∼ N(0, σ2 x)

fit follows fit = ρf · fit−1 + ηf

it · Iit where ηf it ∼ N(0, σ2 f)

Use ǫ = 4, ρa = ρτ = ρf = 0.9 Estimate {σA, σa, στ, σf} by window to fit {σTFPR, σTFPQ, σ∆

I, projection of ln(

βk) on ln(TFPRk)}

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Simulation Results

India

1985–1991 1992–1996 1997–2001 2002–2007 2008–2013 σ2

• τ/σ2

T F P R (our correction)

0.64 0.76 0.76 0.68 0.71 σ2

τ/σ2 T F P R (truth)

0.60 0.80 0.82 0.68 0.71

U.S.

1978–1984 1985–1991 1992–1998 1999–2005 2006–2013 σ2

• τ/σ2

T F P R (our correction)

0.36 0.41 0.34 0.32 0.25 σ2

τ/σ2 T F P R (truth)

0.17 0.29 0.17 0.13 0.02

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Takeaways from simulations

ln( β) vs. ln(TFPR) approach: Does well at correcting for additive measurement error

◮ similar results when measurement error is in revenues ◮ tends to undercorrect when there is lots of measurement error

And further simulations show: Does not correct at all for multiplicative measurement error Does not correct at all for adjustment costs

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Conclusion

Proposed a way to estimate true dispersion of marginal products

◮ Revenue growth is less sensitive to input growth when average

products overstate marginal products

◮ Requires measurement error be additive and ⊥ to distortions

Implemented on Indian ASI

◮ Potential gains from reallocation reduced by 1

5

◮ Time-series volatility reduced by 1

5

Implemented on U.S. LRD

◮ Potential gains from reallocation reduced by 3

5

◮ Time-series volatility reduced by 4

5

◮ No longer a sharp downward trend in allocative efficiency ◮ U.S. allocative efficiency predominantly higher than in India

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Should the U.S. Census Bureau have noticed?

Arguably hard to see: Variance of ln R and ln I rose 7.2% and 7.3% (1978–2013) Correlation of ln R and ln I fell from 0.993 to 0.979 22–58 times higher variance for ln R and ln I than for ln TFPR

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