Misallocation or Mismeasurement? Mark Bils, University of Rochester and NBER Pete Klenow, Stanford University and NBER Cian Ruane, Stanford University February 2017 1 / 68
Motivation Large gaps in average revenue products (TFPR) across plants ◮ Syverson (2011) Huge purported gains from reallocation of inputs ◮ Banerjee & Duflo (2005) ◮ Restuccia & Rogerson (2008) ◮ Hsieh & Klenow (2009, 2014) But big differences in measured average products need not imply big differences in true marginal products 2 / 68
U.S. manufacturing since the 1970s Major increase in TFPR dispersion (Kehrig, 2015) ◮ Implies falling allocative efficiency ◮ If true, lowered TFP growth by about 2.5 percent per year ◮ Cumulated to 55 percent lower TFP by late 2000s ◮ Given measured TFP growth was about 1.7 percent per year, would imply residual TFP growth of 4.2 percent per year Real, or measurement error getting worse? 3 / 68
U.S. Allocative Efficiency & Residual TFP 4 / 68
What we do Propose way to estimate marginal products under: ◮ Measurement error ◮ Misspecification due to overhead costs Apply to: ◮ manufacturing plants in the U.S. 1978–2007 ◮ manufacturing plants in India 1985–2011 Preview of results: ◮ Eliminates the severe decline in U.S. allocative efficiency ◮ Reduces potential gains from reallocation in India by 40% ◮ Leaves U.S. a stable 30% higher allocative efficiency than India 5 / 68
Measurement error in the Indian data Book values instead of market values for capital Number of contract workers not known End-of-previous-year � = beginning-of-current-year stocks Jumps in reported age across years for many plant 6 / 68
Measurement error in the U.S. data Book values instead of market values for capital Census is frequently forced to impute data ◮ SSA, IRS data on a subset of plants, variables ◮ Sometimes impute based on other plants ◮ See White, Reiter and Petrin (2016) for a critique ◮ And Petrin, Rotemberg and White (2017, in progress) 7 / 68
Table of Contents Simple model 1 Full Model 2 Data & Measurement 3 Patterns in the data 4 Test for measurement & specification error 5 Correcting Aggregates 6 8 / 68
Simple model setup �� � 1 �� � 1 − 1 1 − 1 1 ǫ , P = i P 1 − ǫ Y = i Y ǫ 1 − ǫ i i Y i = A i L i max (1 − τ Y i ) P i Y i − wL i ◮ Monopolistic competitor takes w , Y , and P as given � P i Y i ≡ P i Y i + g i � L i ≡ L i + f i 9 / 68
Simple model TFPR P i = markup × marginal cost � � � � ǫ τ i · w 1 P i = × , where τ i ≡ 1 − τ Y ǫ − 1 A i i P i Y i ∝ τ i · L i � � � P i Y i τ i × 1 + g i / ( P i Y i ) TFPR i ≡ ∝ � 1 + f i /L i L i 10 / 68
Numerical example τ i — so the true distortion is fixed over time g i , f i — so additive measurement error is fixed over time A it — so productivity is time-varying � � � PY PY � PY PY L PY L � PY � L L � � L L Firm 1 100 50 2 120 50 2.4 50 25 2 Firm 2 50 50 1 40 50 0.8 25 25 1 11 / 68
Lessons from the numerical example � � P it Y it / � � L it = τ i when constant measurement error, distortions � � � � P it Y it / � � L it on ln ( TFPR ) yields: Regressing ln ◮ 1 if there is no measurement error in TFPR ◮ 0 if all TFPR dispersion is due to measurement error ◮ ∼ 2/3 in the numerical example above Later we generalize in order to: ◮ Allow shocks to measurement error and distortions ◮ Infer the signal from covariance b/w levels, first differences 12 / 68
Projection of First Differences on Levels 13 / 68
Full model vs. Simple model Capital, labor, and intermediates Distortions hitting each input Multiple sectors Shocks to τ and shocks to measurement error Key assumption: measurement error is orthogonal to τ 14 / 68
Table of Contents Simple model 1 Full Model 2 Data & Measurement 3 Patterns in the data 4 Test for measurement & specification error 5 Correcting Aggregates 6 15 / 68
Model (Setup) Closed economy, S sectors, N s firms, L workers, K capital Q = C + X Q = � S s =1 Q θ s s �� N s � 1 1 − 1 1 − 1 ǫ Q s = Q ǫ i si Q si = A si ( K α s si L 1 − α s ) γ s X 1 − γ s si si max R si − (1 + τ L si ) wL si − (1 + τ K si ) rK si − (1 + τ X si ) X si ◮ R si ≡ P si Q si ◮ Monopolistic competitor takes input prices as given 16 / 68
Model (Aggregate TFP) C TFP ≡ L 1 − ˜ α K ˜ α � S s =1 α s γ s θ s ◮ where ˜ α ≡ � S s =1 γ s θ s � S θs � S s =1 γsθs TFP = T × TFP s s =1 ◮ T = reflects sectoral distortions (set aside) Q s ◮ TFP s ≡ ( K α s s L 1 − α s ) γ s X 1 − γ s s s 17 / 68
Model (Sectoral TFP) Suppressing s here and whenever possible: � N � 1 � τ i � 1 − ǫ � ǫ − 1 A ǫ − 1 TFP = i τ i �� � α � γ � � 1 − α � � 1 − γ 1 + τ L 1 + τ K 1 + τ X τ i ≡ i i i �� 1 + τ K � α � γ � 1 + τ L � 1 − α � 1 + τ X � 1 − γ τ ≡ �� N � − 1 where 1 + τ L ≡ R i 1 and so on i =1 R 1+ τ L i 18 / 68
Model (Sectoral TFP Decomposition) 1 TFP = AE · PD · ¯ A · N ǫ − 1 AE ≡ Allocative Efficiency PD ≡ Productivity Dispersion ¯ A ≡ Average productivity 1 ǫ − 1 ≡ Variety N 19 / 68
Model (Sectoral TFP Decomposition) � � � � ǫ − 1 � 1 1 � A i � ǫ − 1 � τ i � A i � 1 − ǫ N N � � ǫ − 1 ǫ − 1 1 1 TFP = × ¯ ˜ N τ N A A i i � �� � � �� � AE = Allocative Efficiency PD s = Productivity Dispersion 1 ¯ × N × A ǫ − 1 � �� � ���� Variety Average Productivity � i ( A i ) ǫ − 1 � 1 � N ˜ 1 ǫ − 1 A = (power mean) N A = � N 1 ¯ i =1 A N (geometric mean) i 20 / 68
Table of Contents Simple model 1 Full Model 2 Data & Measurement 3 Patterns in the data 4 Test for measurement & specification error 5 Correcting Aggregates 6 21 / 68
Indian Annual Survey of Industries (ASI) Survey of Indian Manufacturing Plants ◮ Long panel 1985–2011 ◮ Used in Hsieh and Klenow (2009, 2014) Sampling Frame: ◮ ∼ 43,000 plants per year ◮ All plants > 100 or 200 workers (45% of plant-years) ◮ Probabilistic if > 10 or 20 workers (55% of plant-years) Variables used: ◮ Gross output ( R i ), intermediate inputs ( X i ), labor ( L i ), labor cost ( wL i ), and capital ( K i ) 22 / 68
U.S. Longitudinal Research Database (LRD) U.S. Census Bureau data on manufacturing plants ◮ Long panel, 1978–2007 analyzed so far ◮ Used in Hsieh and Klenow (2009, 2014) Sampling Frame: ◮ Annual Survey of Manufacturing (ASM) plants ◮ ∼ 50k plants with at least one employee ◮ Probabilistic sampling for ∼ 34k plants, certainty for other ∼ 16k Variables used: ◮ Gross output ( R i ), intermediate inputs ( X i ), labor ( L i ), labor cost ( wL i ), and capital ( K i ) 23 / 68
Measurement error in the Indian ASI Frequency Magnitude Age 12.4% 4 years EOY & BOY capital stocks 25.7% 15.4% EOY & BOY goods inventories 22.0% 24.8% EOY & BOY materials inventories 22.3% 20.2% There is measurement error in age if age in year t is not equal to 1 + age in year t − 1 . The magnitude of this measurement error is the median absolute deviation. There is measurement error in stocks and inventories if the deviation of the BOY value in year t from the EOY value in year t − 1 is greater than 1%. The magnitude of this measurement error is the standard deviation of the absolute value of the percentage measurement error. 24 / 68
Data cleaning steps Indian ASI U.S. LRD Step Cleaning Remaining Obs Remaining Obs 1 Starting sample of plant-years 1,159,641 1,767,000 2 Missing no key variables 924,547 1,589,000 3 Common Sector Concordance 899,793 1523,000 4 Trimming extreme TFPR & TFPQ 844,875 1,428,000 The last step trims 1% tails of MRP & TFPQ deviations from sector-year averages 25 / 68
Inferring allocative efficiency from the data � N � 1 − ǫ � 1 � TFPQ i � ǫ − 1 � TFPR i � ǫ − 1 � AE = TFPQ TFPR i � � ǫ � ǫ − 1 R i � A i = TFPQ i = ( � i � ) γ � X 1 − γ L 1 − α K α i i � R i TFPR i = ( � i � ) γ � X 1 − γ L 1 − α K α i i 26 / 68
Inferring allocative efficiency from the data � N � 1 − ǫ � 1 � TFPQ i � ǫ − 1 � TFPR i � ǫ − 1 � AE = TFPQ TFPR i �� N � 1 i TFPQ ǫ − 1 ǫ − 1 TFPQ = i � � � � (1 − α ) γ � � αγ � � 1 − γ ǫ MRP L MRP K MRP X TFPR = ǫ − 1 (1 − α ) γ αγ 1 − γ �� � − 1 � R i 1 ◮ MRPK = and so on � MRPK i R i � ǫ − 1 � � R i ◮ MRPK i = αγ and so on � ǫ K i 27 / 68
Inferring aggregate AE from the data Aggregating within-sector allocative efficiencies: S θst � � S � � s =1 γsθst AE t = AE st s =1 Parameterization: ǫ = 4 based on Redding and Weinstein (2016) α s and γ s inferred from sectoral cost-shares ( r = . 2 ) θ st inferred from sectoral shares of aggregate output 28 / 68
Table of Contents Simple model 1 Full Model 2 Data & Measurement 3 Patterns in the data 4 Test for measurement & specification error 5 Correcting Aggregates 6 29 / 68
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