Key sectors for economic development: A perspective from inter-sectoral linkages and cross-sector misallocation

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1 Key sectors for economic development: A perspective from inter-sectoral linkages and cross-sector misallocation Julio Leal Banco de México ABCDE Conference, 205 Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, 205 / 50

2 Disclaimer The views I will express next do not necessarily represent the views of Banco de México. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

3 Outline Intro 2 Relevant facts Facts 3 Model 4 Calibration 5 Results Results 6 Conclusion Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

4 Motivation Which are the key sectors for economic development? agriculture, manufacturing, or services? What is the role of sector-specific distortions that produce cross-sector misallocation? Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

5 Motivation Which are the key sectors for economic development? agriculture, manufacturing, or services? What is the role of sector-specific distortions that produce cross-sector misallocation? Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

6 What I argue () The productivity of highly interconnected sectors is an important determinant for aggregate productivity. Example: Productivity of refined petroleum affects gasoline production, which in turn affects transportation, which affects trade, which affects refined petroleum products, and so on. It matters: The productivity gap of a single sector with respect to the leader. The degree of interconnections of this sector with the rest of the economy. Definition Akeysectorisonewithalargeproductivitygapandahighdegreeof interconnections. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

7 What I argue () The productivity of highly interconnected sectors is an important determinant for aggregate productivity. Example: Productivity of refined petroleum affects gasoline production, which in turn affects transportation, which affects trade, which affects refined petroleum products, and so on. It matters: The productivity gap of a single sector with respect to the leader. The degree of interconnections of this sector with the rest of the economy. Definition Akeysectorisonewithalargeproductivitygapandahighdegreeof interconnections. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

8 What I argue () The productivity of highly interconnected sectors is an important determinant for aggregate productivity. Example: Productivity of refined petroleum affects gasoline production, which in turn affects transportation, which affects trade, which affects refined petroleum products, and so on. It matters: The productivity gap of a single sector with respect to the leader. The degree of interconnections of this sector with the rest of the economy. Definition Akeysectorisonewithalargeproductivitygapandahighdegreeof interconnections. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

9 What I argue (2) Sector-specific distortions affect aggregate productivity. Create cross-sector misallocation. Reduce the resources available for consumption. The effect of these distortions is also determined by the degree of inter-sectoral linkages. Distortions in highly interconnected sectors have a larger impact on aggregate productivity, than distortions in other sectors. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

10 What I argue (2) Sector-specific distortions affect aggregate productivity. Create cross-sector misallocation. Reduce the resources available for consumption. The effect of these distortions is also determined by the degree of inter-sectoral linkages. Distortions in highly interconnected sectors have a larger impact on aggregate productivity, than distortions in other sectors. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

11 What I do Set-up a multi-sector model. Output of a given sector can be used as an intermediate input for production in other sectors. Introduces a link between the performance of a single sector, and the performance of the rest. Use the model to study three types of distortions per sector: Productivity wedge. Wedge between marginal revenue and marginal cost (a markup). Wedge between the marginal productivity of labor and the marginal cost of labor (MC of labor wedge). Calibrate the model for both, the US and Mexico: Make use of input-output tables. Measure the size of distortions in Mexico relative to the US. Solve for the equilibrium allocation an perform counter-factual exercises. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

12 What I do Set-up a multi-sector model. Output of a given sector can be used as an intermediate input for production in other sectors. Introduces a link between the performance of a single sector, and the performance of the rest. Use the model to study three types of distortions per sector: Productivity wedge. Wedge between marginal revenue and marginal cost (a markup). Wedge between the marginal productivity of labor and the marginal cost of labor (MC of labor wedge). Calibrate the model for both, the US and Mexico: Make use of input-output tables. Measure the size of distortions in Mexico relative to the US. Solve for the equilibrium allocation an perform counter-factual exercises. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

13 What I do Set-up a multi-sector model. Output of a given sector can be used as an intermediate input for production in other sectors. Introduces a link between the performance of a single sector, and the performance of the rest. Use the model to study three types of distortions per sector: Productivity wedge. Wedge between marginal revenue and marginal cost (a markup). Wedge between the marginal productivity of labor and the marginal cost of labor (MC of labor wedge). Calibrate the model for both, the US and Mexico: Make use of input-output tables. Measure the size of distortions in Mexico relative to the US. Solve for the equilibrium allocation an perform counter-factual exercises. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

14 What I do Set-up a multi-sector model. Output of a given sector can be used as an intermediate input for production in other sectors. Introduces a link between the performance of a single sector, and the performance of the rest. Use the model to study three types of distortions per sector: Productivity wedge. Wedge between marginal revenue and marginal cost (a markup). Wedge between the marginal productivity of labor and the marginal cost of labor (MC of labor wedge). Calibrate the model for both, the US and Mexico: Make use of input-output tables. Measure the size of distortions in Mexico relative to the US. Solve for the equilibrium allocation an perform counter-factual exercises. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

15 Network map Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

16 Share of value added in gross output Mexico United States Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

17 Labor income share in GDP, by sector. Figure: Labor income share in value-added United States México Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

18 Model Multi-sector model with N sectors (Long and Plosser, 983, Jones, 20; Acemoglu et al, 202, and others). Supply of labor H is exogenous. Each sector uses labor, and commodities from all sectors (including its own) to produce. There exist three wedges per sector in the economy: Productivity wedge. Markup wedge. MC of labor wedge. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, 205 / 50

19 Technology Production function of a representative firm in sector i : where s i = Â N j= s ij; ands i +( s i )a i <. Resource constraint of each sector j: Final good: Q i = A i (H i ) a i ( s i ) N x s ij ij, () j= Q j = c j + N Â i= x ij,8j =,...,N. Y = c b cb cb N N. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

20 Problem of the final good producer The problem consists on choosing {c i }, taking {p i } as given, to solve: ( max {c i } c b cb cb N N The first order conditions are given by: N Â i= p i c i ). b i (Y /c i ) p i = 0, b i Y = p i c i, 8i. (2) b i = p ic i Y Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

21 Problem of the representative firm in sector i The problem of the representative firm in industry i is given by max H i,{x ij} ( p i A i (H i ) a i( s i ) y i N x s ij j= ij f i wh i... Â N j= p jx ij Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

22 FOCs y i a i ( s i ) p iq i H i = f i w, 8i (3) y i s ij p i Q i x ij = p j, 8i,j (4) Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

23 FOCs y i a i ( s i ) p iq i H i = f i w, 8i (5) y i s ij p i Q i x ij = p j, 8i,j (6) Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

24 Equilibrium aggregate output Equilibrium aggregate output is given by: Y = A Hã where ã and A are constants. Additionally, ln(a )=m 0 a + const where: 2 m 0 a =[m m 2 m 3...m N ] 6 4 lna lna 2 lna lna N Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

25 Vector of influence (or multipliers) Vector of influence: Two terms: m 0 = b 0 (I B) Weights: b Inter-sectoral linkages: (I B). where typical element of B is s ij. Interpretation: a % increase in A i rises aggregate GDP in m i %. dln(y )=m i da i Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

26 Allocation of labor Economy without distortions: Ĥ i H = ˆq i = a i ( s i )m i  N s= a s ( s s )m s Does not depends on relative productivity (A i ). Economy with distortions. H i H = q i = a i ( s i ) yi fi  N s= a s ( s s ) y s f s m i m s where, m = b 0 (I s ij /y i. B),andatypicalelementofNxNmatrix B is If distortions are homogeneous, the allocation of labor is not affected (dispersion is key). Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

27 Allocation of labor Economy without distortions: Ĥ i H = ˆq i = a i ( s i )m i  N s= a s ( s s )m s Does not depends on relative productivity (A i ). Economy with distortions. H i H = q i = a i ( s i ) yi fi  N s= a s ( s s ) y s f s m i m s where, m = b 0 (I s ij /y i. B),andatypicalelementofNxNmatrix B is If distortions are homogeneous, the allocation of labor is not affected (dispersion is key). Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

28 Rents of distortions are lost T = 0 In this case distortions are isomorphic to productivity. y i Q i = y i A i f (H i,{x ij })=c j + Â N i= x ij,8i (7) Effect on aggregate output and productivity could be sizable if resources are not given back. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

29 Removal of a single distortion: Total effect Change in one of the distortions: y i < y 0 i : Y ln = Y 0 N Â j= m j a i ( s i )ln q! j y 0 qj 0 +m i s i ln i yi Effect on the allocation of labor. + N Â j= m 0 m j ( s j )ln i m i (8) It could be positive or negative depending on whether the change in y i reduces the dispersion of wedges. It depends on the degree of influence of each sector m i. 2 Effect on aggregate output through the supply of sector i (positive). 3 Effect on the allocation of gross output into final and intermediate uses (negative). Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

30 Calibration Calibrate the model to Mexico and the US. Use the FOC in each country and data from input-output tables to pin-down the value of the parameters. Assume that the US is a relatively undistorted economy. Common parameters across countries: ( s i )=VA share in the US. a i = Labor share in the US. Use deviations from the 45 degree lines to pin-down y i and f i. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

31 Key sectors Figure: Productivity vs. degree of influence Labor productivity Influence 8 Construction; 30 Business Services; 29 Real Estate; 2 Retail Trade; Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

32 Closing productivity gaps Figure: Effect in Y of closing the productivity gap Leather and Footwear Water Transport Wood Products Post and Telecom. Transport Services Other Non-Metallic Mineral Air Transport Health and Social Work Other Services Basic and Fabricated Metal Machinery, Nec Other Manufacturing Rubber and Plastics Inland Transport Education Utilities Paper, Printing and Pub. Textiles and Textile Products Motor Vehicle and Fuel Trade Financial Intermediation Mining and Quarrying Chemical Products Hotels and Restaurants Electrical and Optical Eq. Transport Equipment Coke and Refined Petroleum Wholesale Trade Retail Trade Food, Beverages and Tobacco Agriculture, forestry & fishing Business Services Real Estate Activities Construction Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

33 Decomposition Figure: Decomposing the effect in Y of closing the productivity gap Effect in logy of closing log productivity gap m T =[,...,]./N m T = β T m T = β T (I B) Change in loga needed to close the productivity gap Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

34 Markup wedge Figure: Calibrated markup values Markup ψ Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

35 Reducing distortions: T > 0 Figure: Effect in Y of reducing markups in Case Effect on Y after closing the markup ψ Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

36 Reducing distortions: T = 0 Figure: Effect in Y of reducing markups in Case 2.2 Effect on Y after closing the markup ψ: Case Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

37 Conclusion Istudiedamodelwithinter-sectorallinkageswithwedgesand calibrated it to match relevant features of the US and México. Ifoundthattheeffectofinter-sectorallinkagesisimportantto determine the gains of closing sectoral productivity gaps. Closing the gap in services gives the biggest gains. Ialsostudiedtheeffectofsector-leveldistortionsandfoundthatits effect could be big depending on whether the rents from distortions stay in the economy or not. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

38 Productivity gap is larger in manufacturing Data from Inklaar and Timmer (202) Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

39 Productivity gap is larger in manufactures Data from Herrendorf and Valentinyi (202) Category Ratio Value Aggregate TFP US /TFP LA 2.30 Services TFPs US /TFPs LA.86 Goods TFPg US /TFPg LA 3.58 Table: Labor share in Mexico Method Description Value Naive Compensation of employees / GDP 0.28 Corrected Compensation of employees/ (Gollin, 200) (GDP-Net Mixed Income-Net indirect taxes) 0.42 Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

40 Related Literature Development literature. Barriers to the use of intermediate inputs in Agriculture (Restuccia et. al, 2008). Barriers to international trade that directly affect industries that produce tradables (Herrendorf and Teixeira, 2005). Financial frictions that affect manufactures more than services. (Buera et. al, 2009). Informality leads to resource misallocation (e.g. Prado, 20, and Moscoso and D Erasmo, 202). Literature that shows that the productivity gap is larger in manufactures than in services. Inklaar and Timmer (202) Herrendorf and Valentinyi (202) Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

41 Problem of the representative firm in sector i The problem of the representative firm in industry i is given by max H i,{x ij},m i ( p i A i (H i ) a i( s i l i ) y i N x s ij ij j= M l i i f i wh i... Â N j= p jx ij p M,i M i Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

42 FOCs y i a i ( s i l i ) p iq i H i = f i w, 8i (9) y i s ij p i Q i x ij = p j, 8i (0) y i l i p i Q i M i = p M,i, 8i () Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

43 FOCs y i a i ( s i l i ) p iq i H i = f i w, 8i (9) y i s ij p i Q i x ij = p j, 8i (0) y i l i p i Q i M i = p M,i, 8i () Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

44 FOCs y i a i ( s i l i ) p iq i H i = f i w, 8i (2) y i s ij p i Q i x ij = p j, 8i (3) y i l i p i Q i M i = p M,i, 8i (4) Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

45 FOCs y i a i ( s i l i ) p iq i H i = f i w, 8i (2) y i s ij p i Q i x ij = p j, 8i (3) y i l i p i Q i M i = p M,i, 8i (4) Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

46 Household problem Problem: max{u(c)} s.t. C = wh + +T where T = Rents from distortions. Resource constraint: If rents from distortions are given back, T > 0:Q j = c j + Â N i= x ij. If rents from distortions are not given back, and T = 0: y Q i j = c j + Â N i= x ij. Given wedges and import prices, a competitive equilibrium consists on quantities Y, {Q i,h i,c i,x ij,m i } N i= ;andpricesw, and{p j}, 8i,j =,...,N; such that: {c i } solves the representative final good producer problem at the equilibrium prices. 2 H i,{x ij } and M i solve sector s i producer problem at the equilibrium prices and taking p M,i as given. 3 Markets for labor, and goods j =,...,N clear. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

47 Equilibrium Characterization: multipliers vs. weights Figure: Multipliers vs. weights Multipliers Betas Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

48 Equilibrium Characterization Assume: t i = 0andy i = f i =. Then: =) s i = N Â j= s ij = s ij = p jx ij p i Q i. N Â j= pj x ij p i Q i NÂ = p j x ij. p i Q i j= is the share of domestic intermediate inputs in gross output. Similarly: s i + l i = ÂN j= p! jx ij + p M,iM i ; (5) p i Q i p i Q i is the share of domestic and imported intermediate inputs in gross output. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

49 Equilibrium Characterization Assume: t i = 0andy i = f i =. Then: =) s i = N Â j= s ij = s ij = p jx ij. p i Q i pj x ij N Â j= p i Q i NÂ = p j x ij. p i Q i j= is the share of domestic intermediate inputs in gross output. Similarly, when y i 6= : ( y i )(s i + l i )= ÂN j= p jx ij p i Q i! + p M,iM i p i Q i ; (6) is the share of domestic and imported intermediate inputs in gross output. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

50 Calibrate distortions Given parameters in the US, I can compute distortions using Mexico s FOC: I match the value added shares in Mexico y i = s i  N j= p j x ij p i Q i! MX =  N j= p! US j x ij p i Q i  N j= p j x ij p i Q i! MX, 8i. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

51 Calibrated distortions Figure: Distortions Markup ( ψ i ) Sectors Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

52 Calibrate productivity gaps, not levels. Problem: we don t have import prices, we can not calculate productivity levels. It can be shown that in equilibrium: ln Q mx i A mx i Qi us µ ln A us, (7) i Since, I observe (Qi mx /Qi us ) there is no need to calibrate productivity levels. Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

53 Calibrate distortions Given parameters in the US, I can compute distortions using Mexico s FOC: I match the value added shares in Mexico y i = s i + l i  N j= p! MX = j x ij pi Q MX + i p i Q i p M,i M i  N j= p j x ij p i Q i  N j= p j x ij p i Q i! US pi Q + i p M,i M i US! MX, 8i. pi Q MX + i p M,i M i Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

54 Calibrated distortions Figure: Distortions Markup ( ψ i ) Marginal cost of labor wedge ( φ i ) Sectors Sectors Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

55 Key sectors (naive definition) Figure: Key Sectors.2 2. Labor Productivity relative to the US (PPP) Multipliers Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

56 Counter-factual exercises Modify the productivity gap in sector i, and compute the change in aggregate output Y : Y A ln Y 0 µ ln i A 0. (8) i Additionally, it can be shown that in equilibrium: ln( Y Y 0 )=f y(y 0 i,y i ), (9) ln( Y Y 0 )=f f (f 0 i,f i ). (20) Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

57 Two typical industries rubber and plastics (manufactures) wholesale and retail trade (services) Productivity Julio Leal (Banco Rubber de México) and plastics Key sectors, is 0 linkages, times more and misallocation productive ABCDE in Conference, the US than 205 in 47 / 50 Closing productivity gaps Figure: Change in A i needed to close the labor productivity gap. Change in TFP needed to close labor productivity gap Labor Productivity relative to the US (PPP)

58 Reducing distortions Figure: Reducing distortions Effect on Y after closing the markup ( ψ i ) Effect on Y after closing the labor wedge ( φ i ) Sectors Sectors Two didactic cases post and telecommunications wholesale and retail trade (services) Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

59 Markups FOC min{wl + rk} st Q = f (k,l) L = wl + rk + l (Q f (k,l)) FOC : l : w lf l = 0 k : r lf k = 0 Reescribir Ec. w lf l = 0 w = lf l Q/Q Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50

60 Conceptual framework Instituciones -Banco de México -SHCP -SCJN -Condusef Políticas - Impuestos - Transf. Sociales - Salud - Combate al narcotráfico Incentivos? Informalidad PIB y Bienestar Capital Trabajo Productividad Asignación de Recursos -Sectores -Empresas -Factores -Ocupaciones Julio Leal (Banco de México) Key sectors, linkages, and misallocation ABCDE Conference, / 50