Using the FLQ formula in estimating interregional output multipliers

Transcription

1 Using the FLQ formula in estimating interregional output multipliers 9. Input-Output Workshop, Bremen M. Jahn 1, T. Tohmo 2, A.T. Flegg 3 1 Hamburg Institute of International Economics, 2 University of Jyväskylä, 3 University of the West of England Bristol

2 Content Introduction 1. Introduction 2. Interregional FLQ M. Jahn 2 / 16

3 Content Introduction 1. Introduction 2. Interregional FLQ M. Jahn 3 / 16

4 Data and literature Data: Survey-based interregional IO table for South Korea (28 sectors, 16 regions) from 2005 (collected by the Bank of Korea): region 1 region 2 sector 1 sector 2 sector 3 sector 1 sector 2 sector 3 sector 1 region 1 sector 2 sector 3 sector 1 region 2 sector 2 sector Interregional FLQ M. Jahn 4 / 16

5 Data and literature Data: Survey-based interregional IO table for South Korea (28 sectors, 16 regions) from 2005 (collected by the Bank of Korea): region 1 region 2 sector 1 sector 2 sector 3 sector 1 sector 2 sector 3 sector 1 region 1 sector 2 sector 3 sector 1 region 2 sector 2 sector Relevant recent literature: Flegg, Tohmo (2018): The regionalization of national input-output tables: a study of South Korean regions, to appear in Papers in Regional Science Jahn (2016): Extending the FLQ formula: a location quotient-based interregional input output framework, Regional Studies 51(10) Interregional FLQ M. Jahn 4 / 16

6 Intraregional input coefficients and multipliers Reminder: Intraregional input-coefficient matrices A rr are defined as: A rr = (aij rr ) = ( zrr ij /xj r ) for r = 1,..., R (1) Notation: zij sr IO transactions from sector i in region s to sector j in region r output of sector j in region r x r j Interregional FLQ M. Jahn 5 / 16

7 Intraregional input coefficients and multipliers Reminder: Intraregional input-coefficient matrices A rr are defined as: A rr = (aij rr ) = ( zrr ij /xj r ) for r = 1,..., R (1) Notation: zij sr IO transactions from sector i in region s to sector j in region r output of sector j in region r x r j FLQ estimate for the intraregional input coefficients: â rr ij = min(a ij, a ij FLQ r ij) = min(a ij, a ij CILQ r ij λ r ) (2) Notation: a ij national input coefficient (without imports, a ij = z ij/x j ) ( ) CILQij r cross-industry location quotient CILQij r = ɛr i/ɛ r j ɛ i/ɛ for i j j ɛ r j size of sector j in region r (often employment or output) ) λ r adjustment for size of region r (λ r = [log 2 (1 + ɛr /ɛ)] δ Interregional FLQ M. Jahn 5 / 16

8 Intraregional multipliers Intraregional output multipliers describe how much output (value) would theoretically be created in the same region through backward linkages (suppliers) if a certain regional industry was affected by an exogenous unit demand shock. Interregional FLQ M. Jahn 6 / 16

9 Intraregional multipliers Intraregional output multipliers describe how much output (value) would theoretically be created in the same region through backward linkages (suppliers) if a certain regional industry was affected by an exogenous unit demand shock. Intraregional Leontief inverse: Intraregional output multiplier: L r = (I A rr ) 1 (3) N r j = i L r (ij) (4) Mathematically, the multiplier is the sum of the column of the Leontief inverse which refers to the respective industry. Interregional FLQ M. Jahn 6 / 16

10 South Korean IRIO table: Previous results Performance of models for the intraregional output multipliers with different specifications of δ (region- and/or sector-specific) in the FLQ formula: method MAPE error var. BIC AIC k N SLQ CILQ FLQ with δ FLQ with δ r FLQ with δ j FLQ with δ jr Information criteria BIC and AIC used to compare error variances for models with different numbers of parameters k Interregional FLQ M. Jahn 7 / 16

11 Content Introduction 1. Introduction 2. Interregional FLQ M. Jahn 8 / 16

12 Definition Introduction Interregional output multipliers describe how much output (value) would theoretically be created in all regions combined through backward linkages (suppliers) if a certain regional industry was affected by an exogenous unit demand shock. Interregional FLQ M. Jahn 9 / 16

13 Definition Introduction Interregional output multipliers describe how much output (value) would theoretically be created in all regions combined through backward linkages (suppliers) if a certain regional industry was affected by an exogenous unit demand shock. Starting with the interregional coefficient matrices A sr = (a sr ij ) = ( zsr ij /x r j ) for s, r = 1,..., R, (5) one way to define the interregional Leontief inverse is: L = (I A) 1 with (6) A A 1R A =..... (7) A R1... A RR Interregional FLQ M. Jahn 9 / 16

14 Definition Introduction Interregional output multipliers describe how much output (value) would theoretically be created in all regions combined through backward linkages (suppliers) if a certain regional industry was affected by an exogenous unit demand shock. Starting with the interregional coefficient matrices A sr = (a sr ij ) = ( zsr ij /x r j ) for s, r = 1,..., R, (5) one way to define the interregional Leontief inverse is: L = (I A) 1 with (6) A A 1R A =..... (7) A R1... A RR Denoting the blocks of L with L sr (similarly to A), the interregional multipliers are defined as M r j = i,s Lsr (ij). Interregional FLQ M. Jahn 9 / 16

15 Empirical importance of interregional IO transactions Intra- and interregional multipliers for 4 of 16 South Korean regions (2005) for 28 sectors: inter intra ratio (inter/intra) region mean std. dev. mean std. dev. mean std. dev. Seoul Busan Gangwon-do Jeju-do total Seoul: north-west coast, Busan: south-east coast, Gangwon-do: mountainous border region in the north, Jeju-do: remote island Interregional FLQ M. Jahn 10 / 16

16 Estimation: Gravity model In order to estimate interregional IO transactions, a gravity model can be used (cf. Jahn, 2016): ln z sr ij = β 0 +β 1 ln x s i +β 2 ln x r j +β 3 ln d sr +β 4 border sr +η sr ij for s r Notation: zij sr xi s xj r d sr border sr η sr ij IO transactions from sector i in region s to sector j in region r output of sending sector output of receiving sector geographical distance between region s and r dummy whether regions share a land border error term Interregional FLQ M. Jahn 11 / 16

17 Estimation: Gravity model In order to estimate interregional IO transactions, a gravity model can be used (cf. Jahn, 2016): ln z sr ij = β 0 +β 1 ln x s i +β 2 ln x r j +β 3 ln d sr +β 4 border sr +η sr ij for s r Notation: zij sr xi s xj r d sr border sr η sr ij IO transactions from sector i in region s to sector j in region r output of sending sector output of receiving sector geographical distance between region s and r dummy whether regions share a land border error term Simple alternative ignoring spatial information (cf. Batten, 1982): ln zij sr = β 0 + β 1 ln xi s + β 2 ln xj r + ηij sr Interregional FLQ M. Jahn 11 / 16

18 South Korea: Gravity model results variable coeff. robust se t value [95% conf.int.] output: sending sec output: receiving sec distance adjacency constant R observations Interregional FLQ M. Jahn 12 / 16

19 South Korea: Gravity model results variable coeff. robust se t value [95% conf.int.] output: sending sec output: receiving sec distance adjacency constant R observations All coefficients have the expected sign and magnitude Alternative definitions of distance don t affect the results The simple model has only slightly less explanatory power (R 2 = 0.457) Interregional FLQ M. Jahn 12 / 16

20 The FLQ formula in the interregional setting Reminder: Estimates of intraregional input coefficients according to the FLQ formula: â rr ij = min(a ij, a ij FLQ r ij) (8) This yields in absolute terms: ẑij rr = âij rr xj r, where x j r known or estimated (usually via ɛ r j ). is either Interregional FLQ M. Jahn 13 / 16

21 The FLQ formula in the interregional setting Reminder: Estimates of intraregional input coefficients according to the FLQ formula: â rr ij = min(a ij, a ij FLQ r ij) (8) This yields in absolute terms: ẑij rr = âij rr xj r, where x j r known or estimated (usually via ɛ r j ). is either Since national transactions z ij are also known, the amount of interregional transactions consistent with the FLQ formula is given by: ε FLQ ij = z ij r ẑ rr ij 0 (9) The non-negativity of this FLQ-residual follows from the fact that â rr ij a ij (proof: Jahn, 2016). Interregional FLQ M. Jahn 13 / 16

22 Consistent estimation of IRIO transactions Combining intraregional (FLQ) and interregional (gravity) estimates, we get as initial estimates: ẑ sr ij = { min(aij, a ij FLQ r ij ) x r j for s = r c ij ( ) (xi s) ˆβ1 (xj r ) ˆβ2 (d sr ) ˆβ3 exp( ˆβ 4 border sr ) for s r. The constant c ij is chosen such that s,r(s r) ẑsr ij = ε FLQ ij. Interregional FLQ M. Jahn 14 / 16

23 Consistent estimation of IRIO transactions Combining intraregional (FLQ) and interregional (gravity) estimates, we get as initial estimates: ẑ sr ij = { min(aij, a ij FLQ r ij ) x r j for s = r c ij ( ) (xi s) ˆβ1 (xj r ) ˆβ2 (d sr ) ˆβ3 exp( ˆβ 4 border sr ) for s r. The constant c ij is chosen such that s,r(s r) ẑsr ij = ε FLQ ij. In order to obtain the final estimates, the following optimization problem is solved: min S = ( z ij sr ẑij sr )2 z ij sr z sr i,j,s,r ij (10) subject to i,s zsr ij xj r and s,r zsr ij = z ij. The FLQ-based intraregional estimates are kept fix z ij rr = ẑij rr in this optimization. Interregional FLQ M. Jahn 14 / 16

24 South Korea: New results Performance of models for the interregional output multipliers with different specifications of δ in the FLQ formula: method MAPE error var. BIC AIC k N FLQ δ + grav FLQ δ j + grav FLQ δ r + grav FLQ δ jr + grav FLQ δ + simple FLQ δ j + simple FLQ δ r + simple FLQ δ jr + simple CILQ + grav CILQ + simple SLQ + grav SLQ + simple Interregional FLQ M. Jahn 15 / 16

25 Conclusions Introduction The most important results: Ignoring interregional IO relations results in much too low multipliers Interregional FLQ M. Jahn 16 / 16

26 Conclusions Introduction The most important results: Ignoring interregional IO relations results in much too low multipliers Estimating interregional IO transactions requires a combination of intra- and interregional models, as well as a balancing algorithm Interregional FLQ M. Jahn 16 / 16

27 Conclusions Introduction The most important results: Ignoring interregional IO relations results in much too low multipliers Estimating interregional IO transactions requires a combination of intra- and interregional models, as well as a balancing algorithm The FLQ formula is also useful in estimating interregional multipliers Interregional FLQ M. Jahn 16 / 16

28 Conclusions Introduction The most important results: Ignoring interregional IO relations results in much too low multipliers Estimating interregional IO transactions requires a combination of intra- and interregional models, as well as a balancing algorithm The FLQ formula is also useful in estimating interregional multipliers The penalization of the number of (free) parameters is important for model comparison Interregional FLQ M. Jahn 16 / 16

29 Conclusions Introduction The most important results: Ignoring interregional IO relations results in much too low multipliers Estimating interregional IO transactions requires a combination of intra- and interregional models, as well as a balancing algorithm The FLQ formula is also useful in estimating interregional multipliers The penalization of the number of (free) parameters is important for model comparison Ignoring spatial information does not lead to a worse approximation of true (interregional) multipliers Interregional FLQ M. Jahn 16 / 16

30 Using the FLQ formula in estimating interregional output multipliers 9. Input-Output Workshop, Bremen M. Jahn 1, T. Tohmo 2, A.T. Flegg 3 1 Hamburg Institute of International Economics, 2 University of Jyväskylä, 3 University of the West of England Bristol Interregional FLQ M. Jahn 16 / 16