Transcript www.euklems.net

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
UK 1995. Use table in purchaser’s prices
EUKLEMS
Use Table at purchasers' prices, 1995
Agri
Agri, mining
Manuf,util,const
trade,transp
others
govt
Taxes (-subs) on production
Compensation of employees
Gross operating surplus
FISIM adjustment
Total output
Taxes (-subs) on products
Manuf trade others govt
C
5794 32553 1612
253
171
10737 234332 40138 32325 29266
1994 12904 47589 23723 4860
5246 51726 44261 91158 52983
0
0
0
0
0
-26 3585 6103 2755 1739
6485 114774 91488 98866 75105
21676 70021 46614 92771 7952
-774 -9614 -5423 15810
0
51132 510282 272383 357660 172077
528
3080
4043
7626
6585
G
I
8695
0
234031
0
67610
0
133031
0
0 157512
443367 157512
51875
0
total
X
domestic M
1287 11899 62264
108627 144435 833891
954 18038 177673
10971 29137 418513
0
0 157512
14156
386718
239034
0
121839 203509
5564
-33
12690
160237
16995
17129
0
GDP=cigxm
207051 719176
GDP=value added
79268
719176
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:
VYjt   PijtX X ijt  LC Ej  OS j  TjO
i
VK j  VLj  LC Ej  OS j  TjO
Or, inputs in basic prices:
VYjt  i pit X ijt  TVijX  TijX  LC Ej  OS j  TjO
Industry sum of Supply table, output in basic price:
VY jt   PijtY Yijt
i
EUKLEMS
Marcel Timmer’s June 23 2005 document:
Interindustry Accounts in EUKLEMS
Row sum of USE table, in purchaser’s price:
VSi  VYi C  VM i   PijX X ij   PifX X if

j
f
f
PifX X if  VCi  VI i  VGi  VEX i
VYi C   j , f PijX X ij   j , f pi X ij  TVi  Ti
Commodity sum of Supply table, in purchaser’s price:
VYi C   j PijY Yij  TR  TT  TV  T
Nominal GDP is sum of value added or sum of final demand:
GDP  VK j  VL j  TV  T
j
GDP  VCi  VIi  VGi  VEX i  VM i
i
EUKLEMS
1
Industries
….
j
….
n
Total
intermediate
use
1
Final demand
….
….
f
Total use
1
:
Commodities
Total intermediate input at purchase price
Capital
Labour
Taxes on production
i
:
m
pxijXij
VXj
OSj
LCEj
TOj
Gross value added at basic price
Gross output at basic prices
VYj
VXi
pXifXif
VUi
EUKLEMS
Industries
1
….
j
….
n
Import
Total
Commodities
1
:
i
pyijYij
:
m
Total
VYj
pmiMi VSi
EUKLEMS
Ingredients 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;
EUKLEMS
2 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:
C
VY
 it  VYjt  TV  T
i
j
2.3 Relation of the different price concepts:
Y
j
X
ij
X
jf
P , P , P , Pi
M
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, TOjt.
EUKLEMS
Table 4. Households final consumption expenditure by COICOP heading in 1995
Full COICOP headings listed in Annex B
Product
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Agriculture
Forestry
Fishing
Coal extraction
Oil and gas extraction
Metal ores extraction
Other mining and quarrying
Meat processing
Fish and fruit processing
Oils and fats
Dairy products
Grain milling and starch
Animal feed
Bread, biscuits etc
Sugar
Confectionery
01.1
01.2
02.1
02.2
03.1
Food
Non-alcoholic
beverages
Alcoholic
beverages
Tobacco
Clothing
6 496
131
17
10 740
5 981
725
7 286
1 357
4 237
314
4 537
784
138
-
-
-
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:
VX ij 0 VX ijT
VYjt
VYitC
1) Initial guess, or target, of USE table for t:
VX ijt(1)  tVX ij 0  (1  t )VX ijT
perhaps including
(1)
O(1)
(1)
LC(1)
,
OS
,
T
,
VC
j
j
j
i ,.....
2) Find USE(t) such that:
VX
O

LC

OS

T
ijt
jt
jt
jt  VY jt
i
VX
j
ijt
 VCit  VIit  VGit  VEX it  VYitC  VM it
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 RAS
4.2 Minimize objective function
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
 VX ij  VX
min  wij 
(1)

VX
i, j
ij

(1)
ij



2
Subject to:
VX
O

LC

OS

T
ijt
jt
jt
jt  VY jt
i
VX
ijt
 VCit  VIit  VGit  VEX it  VYitC  VM it
j
where weights wij may be set according to additional
information about quality of (i,j) data.
EUKLEMS
GAMS implementation of “min sum of squares”
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 ;
EUKLEMS
Implementing “min sum of squares” by using firstorder conditions (Wilcoxen 1988 appendix E3)
Lagrangian:
 VX ij

 VX ij
 1
L   wij 
 rij   2  vij 
 cij 


i
j
i
j
 Ri

 Cj

2
2
1
2
 i ( Ri  VX ij )    j (C j  VX ij )
i
j
j
i
C(j) = column control total; R(i) = row control total
First order conditions:
wij  VX ij
 vij
 rij  

Ri  Ri
 Cj
 VX ij

 cij   i   j


 Cj

which is a linear system in λ and μ and solved immediately
by inverting a matrix (i.e. no iterations to optimize)
EUKLEMS
Method of rAs
Iterate Aij, by alternately scaling the columns and rows to
the column and row control totals.
Start with
Aij(1)
(2)
ij
Scale the columns, j: A
Scale the rows, i:
Cj


Aij(3) 
Repeat until converged:
k
(1)
kj
A
Aij(1)
Ri
(2)
A
ij
k Aik(2)
... Aij( n )
i  1, 2...
j  1, 2...
EUKLEMS
Implementing RAS using metadata and Stata
gen x0=1
*1
sort gen age edu ocp
by gen age edu ocp: egen gaeo1=sum(x0)
gen x11=x0*(gaeo/gaeo1)
sort sec gen age edu
by sec gen age edu: egen sgae1=sum(x11)
gen x12=x11*(sgae/sgae1)
local i=2
local j=1
while `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
}
EUKLEMS
SAS RAS metadata example.
Want
E(gender,age,educ,occupation,sector)
Have Etarget(gender,age,educ,occupation)
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
Implementing RAS directly (not using Metadata)
EUKLEMS
D O
1 0 i t
d o j = 1
s u m = 0
d o i =
s u m =
e n d d o
c s u m (
i f ( c
Q Q =
e l s e
Q Q = 1
e n d i f
d o i =
A p ( i
e n d d o
e n d d o
e r = 1 , I T E R M A X
, n n
d o
s u
d o
s
e n
r s
i f
Q
e l
Q
e n
d o
R
A
S
i
, m m
i = 1
m = 0
j =
u m =
d d o
u m (
( r
Q =
s e
Q = 1
d i f
j =
R =
p ( i
S =
f (
E R R
i f
e n d i
e n d d o
e n d d o
i f
1 0
1 , m m
s u m +
A p ( i , j )
j ) = s u m
s u m ( j ) . N E . 0 ) t h e n
c t o t ( j ) / c s u m ( j )
. 0
1 , m m
, j ) =
A p ( i , j )
1 , n n
s u m +
Q Q
A p ( i , j )
i ) = s u m
s u m ( i ) . N E . 0 ) t h e n
r t o t ( i ) / r s u m ( i )
. 0
1 ,
A
, j
A
S S
=
( S
f
n
p
)
(
.
n
( i
=
i ,
N E
A B
S . L
, j
R
j )
. 0
S (
E .
( E R R 3 . L T .
C O N T I N U E
*
)
R
*
Q Q
) t h e n
1 . 0 - R R / S S )
1 0 . 0 )
E R R 3 = A M A X 1 ( E R R 3 , E R R )
M A X E R R )
g o t o
2 0
! e x i t
i f
c o n v e r g e d
EUKLEMS
Implementing RAS directly; continued
do 10 i
......
do i=1
do j=
BIG
SMAL
if (
ERR
if
if
if
if
if
endi
enddo
enddo
t
.
,
1
=
L
S
(
(
(
(
(
f
er=1,ITERMAX
mm
,nn
AM
=
S.N
= A
SS.
(SS
(SS
(SS
SS.
A
A
E
B
G
.
.
.
L
X
M
.
S
T
G
G
G
E
1
I
0
(
.
T
T
T
.
(
N
)
1
1
.
.
.
1
BIG
1(S
th
.0000
100
100
10.
0.0
,
M
e
R
0
0
.
0
)
Q
A
n
R
.
.
0
)
Q)
LL,QQ)
/SS)
0)
0) .AND.(SS.LE.10000.0))
)
.AND. (SS.LE.1000.0))
.AND. (SS.LE.100.0))
E
E
E
E
E
R
R
R
R
R
R
R
R
R
R
5
4
3
2
1
=
=
=
=
=
A
A
A
A
A
M
M
M
M
M
A
A
A
A
A
X
X
X
X
X
1
1
1
1
1
(
(
(
(
(
E
E
E
E
E
R
R
R
R
R
R
R
R
R
R
5
4
3
2
1
,
,
,
,
,
E
E
E
E
E
R
R
R
R
R
R
R
R
R
R
)
)
)
)
)
ratio = big-small
if (iprint.GE.2) then
write(*,1000) iter,ratio,ERR1,ERR2,ERR3,ERR4,ERR5,Ap(1,1)
endif
if
(ERR3.LT.
10
do
do
A
en
en
ER
ER
ER
ER
ER
CONT
20
CONTINUE
(
d
d
R
R
R
R
R
I
i
j
i
d
d
1
2
3
4
5
N
=
=
,
o
o
L
L
L
L
L
U
1,mm
1,nn
j) =
=
=
=
=
=
E
E
E
E
E
E
R
R
R
R
R
R
R
R
R
R
MAXERR)
goto
20
!exit
loop
if
converged
Ap(i,j)
1
2
3
4
5
!jump
here
if
error
is
small
enough
to
satisfy
conv
crit
EUKLEMS
Example of effects of incompatiable row and column controls
from \2000health\linked\io1976.v00H
1
2
3
4
1 Agriculture
17974.182
4.198
2.838
373.765
2 Non Energy Mining
51.874
469.147
6.132
518.491
3 Coal, Oil and Gas Mining 0.691
11.264 6135.404
1.833
4 Construction
466.222
54.832
250.063
110.157
5 IT manufacturing
109.598
66.625
74.192 1560.156
6 Other Durable Manufacturing
902.525
893.297
841.788 28472.199
7 Petroleum Refining
593.749
92.758
70.708 1360.068
8 Other Nondurable Manufacturing
6547.089
309.406
202.946 10059.084
9 Transportation
1235.378
161.435
168.254 2777.701
10 Communications
165.891
14.784
22.749
452.833
11 Electric, Gas Utilities
344.384
251.699
200.446
185.627
12 Wholesale Trade
1234.294
120.888
113.588 4356.641
13 Retail Trade & Eating 1374.858
143.644
129.137
5203.51
14 Finance
714.393
49.783
261.543
312.531
15 Insurance
762.979
52.708
279.114
324.947
16 Real Estate
1948.969
130.049
718.725
803.057
17 Computer Services
55
13.101
14.927
342.5
18 Business Services ex. Computer
227.488
54.593
68.536 1566.008
19 Other Services
648.497
143.357
160.049
3972.27
20 Government Enterprises 32.641
10.936
6.238
89.676
21 Medical equipment and opthalmic
4.374goods 0.625
1.278
55.747
22 Drugs
192.53
0
0
0.001
23 Offices of health practitioners 0
0
0
0
24 Nursing and personal care facilities
0
0
0
0
25 Hospitals, private
0
0
0
0
26 Health services, nec
0.004
0
0
0
27 Government Hospitals
0
0
0
0
28 Other Govt Health
0
0
0
0
29 Government other than Health 0
0
0
0
30 Households
0
0
0
0
31 nci
5.464
6.36
35.441
102.844
32 va
21203.332 2951.613 12763.505 49185.766
33
0
0
0
0
5
6
7.381
173.758
8.423 4289.012
2.286
638.06
109.284 1902.987
1306.693 6132.446
6000.896 101061.66
37.387
646.279
948.281 12479.656
286.874 6928.369
112.465 1057.161
159.776 3749.012
516.25 6617.188
583.43 7110.254
77.359
749.016
82.251
792.193
203.579 1968.045
40.869
484.213
193.848 3018.148
434.105 5228.511
42.837
515.641
2.679
90.013
0
0.679
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
80.252
898.022
9088.198 109662.2
0
0
7
8
9
10
11
12
13
14
2.621 26564.111
14.196
25.657
24.726
364.763
481.57
37.095
57.808
465.78
17.097
7.689
10.941
3.71
4.849
8.734
5871.352
266.288
12.114
0.006 6748.419
1.097
1.33
0.185
467.032 1088.001 1380.083
554.177 1195.282
689.972
890.088
820.683
12.677
211.58
124.552
224.72
56.576
57.655
72.236
10.797
532.322 10131.11 2142.953
517.751
428.197
812.388
994.164
102.932
1973.385
690.307 1944.372
26.363
450.881
383.253
481.327
35.436
1059.528 68684.766
766.281
175.609
223.464 4420.945 5757.408
241.838
1862.733 6417.223 7783.642
100.167
679.094
968.247 1213.137
162.529
59.935
789.488
680.193 1547.204
94.125 1044.338 1328.042
286.163
1333.868 2864.297
359.78
121.619 4061.791
1073.59 1388.141
128.763
578.325 4826.795
908.503
120.167
183.61 1239.613 1463.086
128.624
597.186 5586.538 1082.646
133.678
197.738 1362.796 1738.194
153.227
117.199
713.405
437.743
145.023
106.535
904.947 1167.996
793.751
123.891
764.128
459.212
150.817
112.17
949.344 1237.602
780.822
303.967 1869.306 1146.243
392.332
278.335 2423.284 3177.302 1981.536
40.582
452.816
182.355
104.605
44.746
336.19
405.109
146.671
173.12
2274.46
753.582
434.462
165.712 2561.323 2386.938
486.45
447.878 5136.667 1770.531 1084.644
397.754 3547.151 4491.725
803.381
36.546
716.686
181.926
92.07
93.573
454.668
584.312
267.535
0.325
7.112
3.304
1.028
2.006
6.029
1.079
0.071
0
335.659
0
17.382
0.486
0.63
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.006
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
95.243 1317.203
980.671
324.558
4.17
143.939
149.969
53.551
4148.279 74895.391 32511.619 19011.875 16862.375 57863.641 74252.008 15216.229
0
0
0
0
0
0
0
0
15
16
34.723
99.103
8.486
22.499
0.178
0.471
764.856 2203.402
8.915
25.768
86.445
272.063
32.329
90.708
213.493
597.442
129.58
366.901
261.544
706.694
115.273
319.846
110.303
321.859
140.5
392.031
692.882 1889.987
782.405 1995.334
1818.195 5190.005
63.892
182.829
283.833 1207.835
721.142 2010.291
225.635
621.228
0.007
3.668
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
40.467
109.635
13948.92 39114.605
0
0
17
5.789
0.283
0.164
32.645
8.802
103.838
8.591
88.37
23.743
30.363
23.384
26.672
35.316
29.088
31.812
74.63
9.217
29.846
110.494
19.168
0.001
0
0
0
0
0
0
0
0
0
2.606
1392.578
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
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
gnp_io.dat