Diusion in the French Input-output Network

Transcription

1 Diusion in the Input-output Contreras Aix-Marseille School of Economics, CNRS, EHESS Getting Inside the Black Box: Technological Evolution Economic Growth Santa Fe Institute Aug

2 Outline 1 Research question 2 Related literature 3 4 Structural Properties 5 Mechanisms in the input-output network 6

3 Motivation Structure determines functionality performance Structure of the economy can be represented by the input-output network: how sectors use output of other sectors as input to produce. Change in structure Technological change due to: 1 Changes in nal dem of HH, Gov't, X, K, 2 Changes in technology

4 Research question How to better capture linkages among sectors how changes in structure impact the macroeconomy through these linkages? Are complex network measures useful tools to identify key sectors in the economy make policy recommendations?

5 Related literature Input-output Analysis: Interdependencies between sectors in an economy or region (Leontief, 1936,1967; Isard, 1951; Hewings et al., 1986). Backward forward linkages, key sectors, structural decomposition (Dietzenbacher Los, 1998; Dietzenbacher, 1992; McGilvray,1977; Rasmussen,1956). Input-output network analysis: properties of the economy (Slater, 1978; Blochlet al., 2011; Xu, 2011; Wen-Qi Duan, 2012) Intersectoral linkages in a multisectoral macroeconomic model (Carvalho, 2010; Acemoglu et al., 2012). s diusion: spread of ideas, innovations, diseases, failures (Kinney et al., 2005; Garal et al., 2010; Lee et al., 2011).

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7 Data Input-output table for for 2007 provided by the INSEE: 116 sectors at current prices in euros

8 The Input-output Model The ow of products from one sector to another is captured in the interindustry transactions table z ij : Output of a sector, x i, is expressed as a function of the dem for inputs, [a ij ] = [z ij /x j ]. In matrix form: x = Ax + DF x = (I A) 1 DF = LDF (1) where x is the production vector, A = [a ij ] is the technical coecients matrix, DF is the nal dem of the exogenous sector (HH, Gov't, exports), L = [l ij ] is the Leontief inverse

9 Input-output Analysis: Linkages Key Sectors An increase in production has two eects: x = x 1 x 0 = LDF 1 LDF 0 = L = I + A + A = (I A) 1 (2) Total Backward linkages: direct indirect eects on dem. Measures the output needed to satisfy additional dem x D BL(total).j = n l ij = (I A) 1 1 (3) i=1 Total Forward linkages: direct indirect eects on supply. Measures additional output available to be used as inputs x S FL(total) i. = n l ij = (I A) 1 1 (4) j=1 Key Sectors: those with both linkages above average

10 The The matrix of technological coecients gives rise to a weighted directed graph with self loops: A=[a ij ]=W=[w ij ] Figure : Construction of the input-output network. Nodes are sectors weighted, directed edges represent economic relationships between sectors.

11 Complex Analysis measures Measures of local centrality: In strength: magnitude of economic relationship between a sector its direct input suppliers s in = j i a ji = A T 1 (5) Out strength: magnitude of economic relationship between a sector its direct input buyers s out = j i a ij = A1 (6) This measures are equivalent to the direct linkage measures proposed in Input-output analysis using the A matrix.

12 Authority Hub Scores Production of sector j increases. Two chains of eects: 1 1. Dem of j for inputs increases; 2. Supply of inputs increase, but to do so sectors increase production; 3. To produce more they dem more inputs: D S D Sector j increases supply of inputs; 2. Dem for inputs increase production increases; 3. Supply of inputs increases: S D S. s(j) j i d(i) i j d(i) (7) s(j) (8) s A d s AA T s (9) d A T s d A T A d (10) This was a 1st round of eects. For higher order eects we iterate this process k, this converges to the principal eigenvectors of AA T A T A.

13 Complex Analysis Measures of global centrality: Authority scores: a buyer that is pointed to by highly ranked (important) suppliers higher order eects on supply X = (I λa T A) 1 1 (11) Hub scores: a supplier that points to highly ranked (important) buyers higher order eects on dem Y = (I λaa T ) 1 1 (12) Authority (hub) scores are the principal eigenvectors of A T A (AA T ). Mutually reinforcing relationship Key sectors: those with the highest authority score, hub score, or both.

14 Structural properties of the input-output network

15 , 2007 Figure : Topology

16 , 2007 Figure : input-output network. 25 percent largest transactions. Sectors' size color is production level in million Euro.

17 Properties of the, 2007 Figure : Strength Distributions

18 Properties of the, 2007 Figure : Authority hub scores

19 Key Sectors,

20 Diusion Distribution of eect of a shock: An increase in output has eects on supply an dem which diuse among sectors. If sector k received the shock: 0<D<1 D D k = 1 ( n j=1 (l jk / n l jk ) 2 ) (13) j=1 Low D more concentrated eect on one or few sectors

21 Diusion of Eect Aggregate Impact of Shock Figure : Aggregate eect on production concentration of the eect

22 Diusion of Eect of a Targeted shock, Figure : Diusion of aggregate eect among sectors. Peacks show a high concentration of the eect.

23 Mechanisms Avalanches: number of sectors aected by a propagating shock Shock on nal dem Shock on technology

24 Mechanisms in IO model IO Model: how is a shock on nal dem spread throughout the economy? Sector j is part of an avalanche triggered by sector i if: eect j = (x i j x j )/ n x i j = l ji / j=1 n l ji > threshold (14) where x i is production of j after a shock on nal dem of i, x j j is original production of j, l ji is the element of the jth row ith column of the L matrix (IO Model). j=1 normalized shock = 1 ( a unit increase in nal dem) A matrix remains xed

25 Avalanche Size with IO Model, Figure : Avalanche size distribution according to dierent thresholds. Largest avalanches triggered by home appliances, weapons ammunitions, automobile equipment

26 A shock on technology Model 1. How is a shock on technology spread from one sector to another? (Kinney et al., 2005; Lee et al., 2011) Node attribute: capacity x i = each sector's production Edge attribute: weight w ij = z ij economic transaction FD xed shock = f w ij is the same for all sectors A shock hits sector i. As a result, the supply dem of inputs of sector i decrease by a fraction f. w ij = (1 f )w ij, 0 < f < 1 (15) The shock spreads to j if: (w jk + w kj ) > (t/f ) x j (16) k N(j) where t: capacity threshold, 0<t<1

27 Avalanche Size with Model 1, Figure : Avalanche size distribution according to dierent f/t. Largest avalanches triggered by nancial, oil rening construction

28 A shock on technology Model 2. A sector gets hit by a shock, then, its input supply dem decrease by a fraction f. Following, production level gets updated according to the input-output model (w ij = (1 f )w ij a ij = z ij /x j). x = (1 A ) 1 DF (17) Finally, the shock spreads to other sectors according to the same rule: if sector i received the original shock, for j in the neighbourhood of i, if: (w jk + w kj ) > (t/f ) x j (18) k N(j) the shock spreads to j.

29 Avalanche Size with Model 2, Figure : Avalanche size distribution according to dierent f/t updating in production. Largest avalanches triggered by nancial, oil rening, electricity

30 Structural properties Asymmetrical structure where sectors have dierent roles are organized in a hierarchy which allows the identication of key sectors. Sectors with the widest diusion of eect a high aggregate eect on production have the highest authority /or hub scores but not necessarily the highest (IO) linkages. Authority scores: higher order eects on supply of inputs. Hub scores: higher order eects on intermediate dem of inputs.

31 on Mechanisms IO model: every sector triggers large avalanches of same size (107 sectors) Model 1: heterogeneous but predominantly large avalanches Model 2: P(A>85%) decreased, but P(A<50%) increased more small-med avalanches; P(50%<A<85%) mixed results Capacity threshold weights distribution are stronger determinants of spreading. Sectors that triggered the largest avalanches using model 1 are the same as using model 2 but dierent from IO model: nancial, oil rening, construction.

32 Authority hub scores provide additional information taking into account higher order eects on supply dem ranking of sectors. Identication of key sectors in the economy leads to policy recommendations: Good hubs that have high aggregate eect good diusion of a shock on FD Triggers of large avalanches or good spreaders of a shock on technology Advantages of applying network analysis: spreading of a shock on technology dierent from spreading of a shock on nal dem beyond model Analysing the structure of the economy how it reacts to shocks as a rst step to model its evolution.

33 Thank you for your attention!