Top Banner
EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks -Necessary input -simple RAS method -minimizing deviations methods
21

EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

Dec 10, 2015

Download

Documents

Jacob Gordon
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

EUKLEMS, Groningen, 15 Sept 2005

Workshop: Inter Industry Accounts, WP1

Mun HoKSG, Harvard University

Interpolation of IO Tables from benchmarks-Necessary input-simple RAS method-minimizing deviations methods

 

Page 2: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

Use Table at purchasers' prices, 1995total

Agri Manuf trade others govt C G I X domestic MAgri, mining 5794 32553 1612 253 171 8695 0 1287 11899 62264 12690Manuf,util,const 10737 234332 40138 32325 29266 234031 0 108627 144435 833891 160237trade,transp 1994 12904 47589 23723 4860 67610 0 954 18038 177673 16995others 5246 51726 44261 91158 52983 133031 0 10971 29137 418513 17129govt 0 0 0 0 0 0 157512 0 0 157512 0Taxes (-subs) on production -26 3585 6103 2755 1739 14156Compensation of employees 6485 114774 91488 98866 75105 386718Gross operating surplus 21676 70021 46614 92771 7952 239034FISIM adjustment -774 -9614 -5423 15810 0 0 GDP=cigxmTotal output 51132 510282 272383 357660 172077 443367 157512 121839 203509 207051 719176

GDP=value addedTaxes (-subs) on products 528 3080 4043 7626 6585 51875 0 5564 -33 79268 719176

UK 1995. Use table in purchaser’s prices

Page 3: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS Marcel Timmer’s June 23 2005 document:Interindustry Accounts in EUKLEMS

Column sum of USE table, output in basic price, inputs in purchaser’s prices:

X E Ojt ijt ijt j j j

i

VY P X LC OS T

Industry sum of Supply table, output in basic price:

Yjt ijt ijt

i

VY P Y

E Oj j j j jVK VL LC OS T

Or, inputs in basic prices:

X X E Ojt it ijt ij ij j j ji

VY p X TV T LC OS T

Page 4: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS Marcel Timmer’s June 23 2005 document:Interindustry Accounts in EUKLEMS

Row sum of USE table, in purchaser’s price:C X X

i i i ij ij if ifj f

VS VY VM P X P X

Commodity sum of Supply table, in purchaser’s price:

C Yi ij ijj

VY P Y TR TT TV T

Xif if i i i if

P X VC VI VG VEX

Nominal GDP is sum of value added or sum of final demand:

j jj

GDP VK VL TV T

i i i i ii

GDP VC VI VG VEX VM

, ,

C Xi ij ij i ij i ij f j f

VY P X p X TV T

Page 5: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

1 …. j …. n 1 …. …. f1:

Commodities i pxijXij VXi VUi:

m

Total intermediate input at purchase price VXj

Capital OSj

Labour LCEj

Taxes on production TOj

Gross value added at basic price

Gross output at basic prices VYj

Industries

pXifXif

Total intermediate

use Total use

Final demand

Page 6: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

Industries1 …. j …. n Import Total

Commodities1:

i pyijYij pmiMi VSi

:m

Total VYj

Page 7: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMSIngredients for interpolation from benchmarks:

1. Benchmarks on the same definitions

2. Time series for industry output, or commodity output, or both; VY(j,t) VYC(i,t)

3. Time series for final demand, C,I,G,X,M

4. Any other time series, e.g. value added by industry VK(j),VL(j); energy input by industry;

Page 8: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS2 Time series data on industry output,

commodity output

2.1 If you have industry output, but not commodity, then first get it using an assumed Supply table:

VYC = [S] (VY+TV+T)

2.2 If you have both, then they must be consistent:

2.3 Relation of the different price concepts:

Cit jt

i j

VY VY TV T

, , ,Y X X Mj ij jf iP P P P

Page 9: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

3 From the National Accounts (C,I,G) derive the time series of VCit , VIit, VGit, VEXit, VMit for as many different commodities as possible. This involves linking National a/c categories to IO categories via bridge tables.

4 From the National a/c derive the value added components by industry: LCjt, OSjt, TO

jt.

Page 10: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

Table 4. Households final consumption expenditure by COICOP heading in 1995

Full COICOP headings listed in Annex B

01.1 01.2 02.1 02.2 03.1

Product FoodNon-alcoholic

beveragesAlcoholic

beverages Tobacco Clothing

1 Agriculture 6 496 - - - -2 Forestry - - - - -3 Fishing 131 - - - -4 Coal extraction - - - - -5 Oil and gas extraction - - - - -6 Metal ores extraction - - - - -7 Other mining and quarrying 17 - - - -8 Meat processing 10 740 - - - -9 Fish and fruit processing 5 981 784 - - -10 Oils and fats 725 - - - -11 Dairy products 7 286 - - - -12 Grain milling and starch 1 357 - - - -13 Animal feed - - - -14 Bread, biscuits etc 4 237 - - - -15 Sugar 314 - - - -16 Confectionery 4 537 138 - - -

Page 11: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS Interpolating the USE table

Denote the benchmark USE table for years 0 and T, and the time series for the column and row totals:

1) Initial guess, or target, of USE table for t:

perhaps including

2) Find USE(t) such that:

0ijVX ijTVXjtVY C

itVY

(1)0 (1 )ijt t ij t ijTVX VX VX

Oijt jt jt jt jt

i

VX LC OS T VY C

ijt it it it it it itj

VX VC VI VG VEX VY VM

(1) (1) (1) (1), , , ,.....Oj j j iLC OS T VC

Page 12: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

3 In the interpolation process we can allow everything to change, or, keep some items fixed. E.g. keep value added and CIGXM fixed and only allow VXij to change.

4. Methods to estimate new matrix.4.1 RAS4.2 Minimize objective function

Page 13: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS Method of minimizing some deviation function.E.g. sum of squared deviations of shares.e.g. where value added and final demand are assumed to be correct

2(1)

(1),

min ij ijij

i j ij

VX VXw

VX

Subject to:

Oijt jt jt jt jt

i

VX LC OS T VY C

ijt it it it it it itj

VX VC VI VG VEX VY VM where weights wij may be set according to additional information about quality of (i,j) data.

Page 14: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

MINP(j).. mpt(j) =E= SUM(ii, Apt(ii,j)) ; IRATIO(ip).. res(ip) =E= (1-alpha*R(ip))*m_x(ip)*xpt(ip) - mpt(ip) ; IRATIO_N(in).. (1-alpha*R(in))*m_x(in)*xpt(in) - mpt(in) =E= 0 ; CBAL(j).. xpt(j) - mpt(j) - VA92(j) =E= 0 ; RBAL(ii).. xpt(ii) - SUM(j, Apt(ii,j)) - yt(ii) =E= 0 ; RBAL29.. yt("IND29") =E= xpt("IND29") ; DEVSQR.. SSR =E= SUM( (ii,j)$wt(ii,j) , SQR((Apt(ii,j) - Atar(ii,j))/Atar(ii,j))) + SUM( ip, SQR(res(ip))/xtar(ip) ) ;

MODEL BAL / ALL /;

**** initialize the guess of A' x' Apt.L(ii,j) = At(ii,j) ; xpt.L(jj) = X92(jj) ; mpt.L(jj) = SUM(i, At(i,jj));

* require solution to be positive OR when known to be zero Apt.LO(ii,j) = 0.0 ; Apt.UP("IND3","IND1") = 0.0 ; ......

SOLVE BAL USING NLP MINIMIZING SSR ;

GAMS implementation of “min sum of squares”

Page 15: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMSImplementing “min sum of squares” by using first-order conditions (Wilcoxen 1988 appendix E3)

22

1 12 2

ij ijij ij ij ij

i j i ji j

VX VXL w r v c

R C

( ) ( )i i ij j j iji j j i

R VX C VX

C(j) = column control total; R(i) = row control totalFirst order conditions:

ij ij ij ijij ij i j

i i j j

w VX v VXr c

R R C C

which is a linear system in λ and μ and solved immediately by inverting a matrix (i.e. no iterations to optimize)

Lagrangian:

Page 16: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS Method of rAs

Iterate Aij, by alternately scaling the columns and rows to the column and row control totals.

Start with (1)ijA

Scale the columns, j:(2) (1)

(1)1,2...j

ij ijkjk

CA A i

A

Scale the rows, i: (3) (2)(2)

1,2...iij ij

ikk

RA A j

A

Repeat until converged: ( )... nijA

Page 17: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMSImplementing RAS using metadata and Stata

gen x0=1*1sort gen age edu ocpby gen age edu ocp: egen gaeo1=sum(x0)gen x11=x0*(gaeo/gaeo1)

sort sec gen age eduby sec gen age edu: egen sgae1=sum(x11)gen x12=x11*(sgae/sgae1)

local i=2local j=1while `i'<=50 { sort gen age edu ocp by gen age edu ocp: egen gaeo`i'=sum(x`j'2) gen x`i'1=x`j'2*(gaeo/gaeo`i') sort sec gen age edu by sec gen age edu: egen sgae`i'=sum(x`i'1) gen x`i'2=x`i'1*(sgae/sgae`i')

local i=`i'+1 local j=`j'+1}

Page 18: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

gen age edu ocp 1 1 1 1 0.02 1 1 1 2 1.38 1 1 1 3 396.54 1 1 1 4 76.91 1 1 2 1 1.61 1 1 2 2 62.15 1 1 2 3 11261.73 1 1 2 4 1231.34 1 1 3 1 19.69 1 1 3 2 349.73 1 1 3 3 27609.01

SAS RAS metadata example. Want E(gender,age,educ,occupation,sector)Have Etarget(gender,age,educ,occupation)

Page 19: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMSImplementing RAS directly (not using Metadata)

DO 10 iter=1,ITERMAX do j=1,nn sum=0 do i=1,mm sum=sum + Ap(i,j) enddo csum(j) = sum if (csum(j).NE.0) then QQ = ctot(j)/csum(j) else QQ=1.0 endif do i=1,mm Ap(i,j) = Ap(i,j) * QQ enddo enddo

do i=1,mm sum=0 do j=1,nn sum=sum + Ap(i,j) enddo rsum(i) = sum if (rsum(i).NE.0) then QQ = rtot(i)/rsum(i) else QQ=1.0 endif do j=1,nn RR = Ap(i,j) * QQ Ap(i,j) = RR SS = A(i,j) if (SS.NE.0) then ERR = ABS(1.0-RR/SS) if (SS.LE.10.0) ERR3=AMAX1(ERR3,ERR) endif enddo enddo if (ERR3.LT. MAXERR) goto 20 !exit if converged 10 CONTINUE

Page 20: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

do 10 iter=1,ITERMAX ....... do i=1,mm do j=1,nn BIG = AMAX1(BIG,QQ) SMALL = AMIN1(SMALL,QQ) if (SS.NE.0) then ERR = ABS(1.0-RR/SS) if (SS.GT.10000.0) ERR5=AMAX1(ERR5,ERR) if ((SS.GT.1000.0) .AND.(SS.LE.10000.0)) ERR4=AMAX1(ERR4,ERR) if ((SS.GT.100.0) .AND. (SS.LE.1000.0)) ERR3=AMAX1(ERR3,ERR) if ((SS.GT.10.0) .AND. (SS.LE.100.0)) ERR2=AMAX1(ERR2,ERR) if (SS.LE.10.0) ERR1=AMAX1(ERR1,ERR) endif enddo enddo

ratio = big-small if (iprint.GE.2) then write(*,1000) iter,ratio,ERR1,ERR2,ERR3,ERR4,ERR5,Ap(1,1) endif if (ERR3.LT. MAXERR) goto 20 !exit loop if converged do i=1,mm do j=1,nn A(i,j) = Ap(i,j) enddo enddo ERR1L=ERR1 ERR2L=ERR2 ERR3L=ERR3 ERR4L=ERR4 ERR5L=ERR510 CONTINUE

20 CONTINUE !jump here if error is small enough to satisfy conv crit

Implementing RAS directly; continued

Page 21: EUKLEMS EUKLEMS, Groningen, 15 Sept 2005 Workshop: Inter Industry Accounts, WP1 Mun Ho KSG, Harvard University Interpolation of IO Tables from benchmarks.

EUKLEMS

from \2000health\linked\io1976.v00H

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 171 Agriculture 17974.182 4.198 2.838 373.765 7.381 173.758 2.621 26564.111 14.196 25.657 24.726 364.763 481.57 37.095 34.723 99.103 5.7892 Non Energy Mining 51.874 469.147 6.132 518.491 8.423 4289.012 57.808 465.78 17.097 7.689 10.941 3.71 4.849 8.734 8.486 22.499 0.2833 Coal, Oil and Gas Mining 0.691 11.264 6135.404 1.833 2.286 638.06 5871.352 266.288 12.114 0.006 6748.419 1.097 1.33 0.185 0.178 0.471 0.1644 Construction 466.222 54.832 250.063 110.157 109.284 1902.987 467.032 1088.001 1380.083 554.177 1195.282 689.972 890.088 820.683 764.856 2203.402 32.6455 IT manufacturing 109.598 66.625 74.192 1560.156 1306.693 6132.446 12.677 211.58 124.552 224.72 56.576 57.655 72.236 10.797 8.915 25.768 8.8026 Other Durable Manufacturing902.525 893.297 841.788 28472.199 6000.896 101061.66 532.322 10131.11 2142.953 517.751 428.197 812.388 994.164 102.932 86.445 272.063 103.8387 Petroleum Refining 593.749 92.758 70.708 1360.068 37.387 646.279 1973.385 690.307 1944.372 26.363 450.881 383.253 481.327 35.436 32.329 90.708 8.5918 Other Nondurable Manufacturing6547.089 309.406 202.946 10059.084 948.281 12479.656 1059.528 68684.766 766.281 175.609 223.464 4420.945 5757.408 241.838 213.493 597.442 88.379 Transportation 1235.378 161.435 168.254 2777.701 286.874 6928.369 1862.733 6417.223 7783.642 100.167 679.094 968.247 1213.137 162.529 129.58 366.901 23.743

10 Communications 165.891 14.784 22.749 452.833 112.465 1057.161 59.935 789.488 680.193 1547.204 94.125 1044.338 1328.042 286.163 261.544 706.694 30.36311 Electric, Gas Utilities 344.384 251.699 200.446 185.627 159.776 3749.012 1333.868 2864.297 359.78 121.619 4061.791 1073.59 1388.141 128.763 115.273 319.846 23.38412 Wholesale Trade 1234.294 120.888 113.588 4356.641 516.25 6617.188 578.325 4826.795 908.503 120.167 183.61 1239.613 1463.086 128.624 110.303 321.859 26.67213 Retail Trade & Eating 1374.858 143.644 129.137 5203.51 583.43 7110.254 597.186 5586.538 1082.646 133.678 197.738 1362.796 1738.194 153.227 140.5 392.031 35.31614 Finance 714.393 49.783 261.543 312.531 77.359 749.016 117.199 713.405 437.743 145.023 106.535 904.947 1167.996 793.751 692.882 1889.987 29.08815 Insurance 762.979 52.708 279.114 324.947 82.251 792.193 123.891 764.128 459.212 150.817 112.17 949.344 1237.602 780.822 782.405 1995.334 31.81216 Real Estate 1948.969 130.049 718.725 803.057 203.579 1968.045 303.967 1869.306 1146.243 392.332 278.335 2423.284 3177.302 1981.536 1818.195 5190.005 74.6317 Computer Services 55 13.101 14.927 342.5 40.869 484.213 40.582 452.816 182.355 104.605 44.746 336.19 405.109 146.671 63.892 182.829 9.21718 Business Services ex. Computer227.488 54.593 68.536 1566.008 193.848 3018.148 173.12 2274.46 753.582 434.462 165.712 2561.323 2386.938 486.45 283.833 1207.835 29.84619 Other Services 648.497 143.357 160.049 3972.27 434.105 5228.511 447.878 5136.667 1770.531 1084.644 397.754 3547.151 4491.725 803.381 721.142 2010.291 110.49420 Government Enterprises 32.641 10.936 6.238 89.676 42.837 515.641 36.546 716.686 181.926 92.07 93.573 454.668 584.312 267.535 225.635 621.228 19.16821 Medical equipment and opthalmic goods4.374 0.625 1.278 55.747 2.679 90.013 0.325 7.112 3.304 1.028 2.006 6.029 1.079 0.071 0.007 3.668 0.00122 Drugs 192.53 0 0 0.001 0 0.679 0 335.659 0 17.382 0.486 0.63 0 0 0 0 023 Offices of health practitioners 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 024 Nursing and personal care facilities0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 025 Hospitals, private 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 026 Health services, nec 0.004 0 0 0 0 0 0 0 0.006 0 0 0 0 0 0 0 027 Government Hospitals 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 028 Other Govt Health 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 029 Government other than Health 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 030 Households 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 031 nci 5.464 6.36 35.441 102.844 80.252 898.022 95.243 1317.203 980.671 324.558 4.17 143.939 149.969 53.551 40.467 109.635 2.60632 va 21203.332 2951.613 12763.505 49185.766 9088.198 109662.2 4148.279 74895.391 32511.619 19011.875 16862.375 57863.641 74252.008 15216.229 13948.92 39114.605 1392.57833 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

VQI 56796 6007 22528 112187 20325 276193 19896 217069 55644 25314 32423 81614 103668 22647 20484 57744 2087

control vqivqc.dat 56796 6007 22528 112187 20325 276193 19896 217069 55644 25314 32423 81614 103668 22647 20484 57744 2087

gnp_io.dat

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Example of effects of incompatiable row and column controls