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. 1 / 65
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) 2 / 65
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 3 / 65
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? 4 / 65
U.S. allocative efficiency 5 / 65
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% 6 / 65
U.S. vs India corrected allocative efficiency 7 / 65
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) 8 / 65
Outline Illustrative example 1 Full model 2 TFPR dispersion in U.S. and Indian data 3 Estimating measurement and specification error 4 Corrected measures of misallocation 5 9 / 65
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 � � 1 − τ Y P i Y i − wL i max 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 10 / 65
Simple model TFPR � � � � 1 ǫ τ i · w P i = × , where τ i ≡ ǫ − 1 1 − τ Y A i i P i Y i ∝ τ i L i � � P i Y i P i Y i · L i TFPR i ≡ ∝ τ i · � � P i Y i L i L i Let ∆ X t ≡ X t − X t − 1 for variable X X t − 1 11 / 65
Identifying misallocation vs. dispersion in TFPR τ i ∆ � PY i = ∆ � L i · TFPR i ◮ assuming distortions and measurement error are fixed over time ◮ in which case ∆ P i Y i = ∆ L i = ( ǫ − 1) ∆ A i 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 τ i | ln TFPR i ) ◮ Validate approach using simulations 12 / 65
Outline Illustrative example 1 Full model 2 TFPR dispersion in U.S. and Indian data 3 Identifying measurement and specification error 4 Corrected misallocation 5 13 / 65
Full Model (Setup) Closed economy, S sectors, N s firms, L workers, K capital �� N s � 1 Q = � S 1 − 1 1 − 1 s =1 Q θ s ǫ Q s = s , Q ǫ i si ) γ s X 1 − γ s Q si = A si ( K α s si L 1 − α 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 X = � S � N s C = Q − X , X si s i 14 / 65
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 Q s ◮ TFP s ≡ ) γ s X 1 − γ s ( K α s s L 1 − α s s s ◮ T = reflects sectoral distortions (set aside) 15 / 65
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 16 / 65
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 17 / 65
Model (Sectoral TFP Decomposition) � � � � ǫ − 1 � � A i � ǫ − 1 � τ i 1 � A i 1 � 1 − ǫ � N � N ǫ − 1 ǫ − 1 1 1 TFP = × � N τ N A A i i � �� � � �� � AE = Allocative Efficiency PD = Productivity Dispersion 1 × N × A ǫ − 1 � �� � ���� Variety Average Productivity � i ( A i ) ǫ − 1 � � N 1 � ǫ − 1 1 A = (power mean) N A = � N 1 i =1 A N (geometric mean) i 18 / 65
Full Model (Sectoral TFP Decomposition) Q TFP ≡ ( L 1 − α K α ) γ X 1 − γ � � � N � 1 1 � A i � ǫ − 1 � τ i � 1 − ǫ N � ǫ − 1 � ǫ − 1 1 ( A i ) ǫ − 1 = × � N τ A i i � �� � � �� � AE = Allocative Efficiency Residual Productivity �� � α � γ � � 1 − α � � 1 − γ 1 + τ L 1 + τ K 1 + τ X τ i ≡ i i i 19 / 65
Aside: Intuition in a special case If A i and τ i are jointly lognormal and τ L i = τ K = τ X then i i AE = ǫ 2 · Var [ ln ( τ i )] 20 / 65
Outline Illustrative example 1 Full model 2 TFPR dispersion in U.S. and Indian data 3 Identifying measurement and specification error 4 Corrected misallocation 5 21 / 65
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 ( R i ), intermediate inputs ( X i ), labor ( L i ), wage bill ( wL i ), and capital ( K i ) 22 / 65
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 ( R i ), intermediate inputs ( X i ), labor ( L i ), wage bill ( wL i ), and capital ( K i ) 23 / 65
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 24 / 65
Inferring allocative efficiency a la Hsieh & Klenow (2009) � N � 1 − ǫ � � TFPQ i � ǫ − 1 � TFPR i 1 � ǫ − 1 AE = TFPQ TFPR i ǫ ( R i ) ǫ − 1 A i = TFPQ i = i L 1 − α ) γ X 1 − γ ( K α i i R i TFPR i = ) γ X 1 − γ i L 1 − α ( K α i i 25 / 65
Inferring allocative efficiency as in Hsieh & Klenow (2009) � N � 1 − ǫ � 1 � TFPQ i � ǫ − 1 � TFPR i � ǫ − 1 AE = TFPQ TFPR i �� N � 1 ǫ − 1 i TFPQ ǫ − 1 TFPQ = i � � � � (1 − α ) γ � � αγ � � 1 − γ ǫ MRPL MRPK MRPX TFPR = ǫ − 1 (1 − α ) γ αγ 1 − γ �� � − 1 R i 1 ◮ MRPK = and so on R MRPK i i � ǫ − 1 � αγ R i ◮ MRPK i = and so on ǫ K i 26 / 65
Inferring aggregate AE 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 27 / 65
Indian allocative efficiency 28 / 65
U.S. allocative efficiency 29 / 65
Allocative efficiency in the U.S. relative to India 30 / 65
TFPR Dispersion in the U.S. and India over time 31 / 65
TFPQ Dispersion in the U.S. and India over time 32 / 65
Recommend
More recommend
