APPENDIX E        THE KALMAN FILTER


This is a summary of 6.1. 
Suppose :
       Observation model:

Yt = Xt . Bt + vt       where vt is N(0,Vt)       eq. 6.1.1 

       Parameter model:

Bt = H . Bt-1 + wt       where wt is N(0,Wt)       eq. 6.1.2 

Then Bt is N(MEt,CEt), where MEt and CEt are given by :

       Forecast parameters :

MFt = H . MEt-1	       	       	       	       eq. 6.1.3 

CFt = H . CEt-1 . HT + Wt       	       	       eq. 6.1.4 

       Forecast dependent variable :

YFt = Xt . MFt       	       	       	       	       eq. 6.1.5 

Var(YFt) = Xt . CFt . XTt + Vt       	       	       eq. 6.1.6 

       Kalman Gain :

Gt = CFt . XTt . (Var(YFt))-1       	       	       eq. 6.1.7 

       Update parameter estimates :

MEt = MFt + Gt . (Yt - YFt)       	       	       eq. 6.1.8 

CEt = CFt - Gt . Xt . CFt       	       	       eq. 6.1.9 


'Data! Data! Data!' he cried impatiently. 'I can't make 
bricks without clay.'  The Copper Beeches, Sir Arthur 
Conan Doyle.

APPENDIX F  THE DATA USED

THE DATA FOR CHAPTERS 5, 8 AND 10


In each table there are observations of the seven 
variables: population, total consumer expenditure in 
money terms, the consumer price deflator, the price of 
wool, the price of synthetic fibre, net domestic 
consumption of wool and total fibre consumption, in that 
order.  These observations run from 1960 to 1978, except 
for fibre prices, which run from 1959 to 1978.

POP is total population, in millions.  

PCE is personal consumption expenditure in millions of 
local currency units, at current prices.

CPI is the consumer price index, 1975=1.0. The source 
of POP, PCE and CPI is "International Financial 
Statistics", published by the International Monetary 
Fund.

PW is the UK cif price of 64's wool, clean basis, 
converted to local currencies per kilogram using period 
average exchange rates from "International Financial 
Statistics".  The US price is increased by $0.56 to allow 
for the tariff.  The source is Hughes, 1976.

PS is the price of polyester staple, 4-6 denier, in local 
currencies per kilogram.  Dutch prices were used for 
Belgium.  The source is Hughes, 1976.



NDC is the net consumption of virgin wool at consumer 
level, in millions of kilograms.  The source is IWS 
(International Wool Secretariat) estimates.

TFC is consumption of wool-type fibres (i.e. wool, 
acrylic, polyester and nylon) at consumer level.  The 
source is IWS estimates.
                         BELGIUM

 POP     PCE     CPI     PW      PS      NDC     TFC

1.      1.      1.      9.203   9.47    1.      1.
9.15    391.    .497    9.003   9.96    21.9    83.2
9.18    408.    .502    8.732   9.23    22.5    85.7
9.22    429.    .509    9.066   8.76    21.0    88.2
9.29    465.    .520    10.284  8.39    24.1    92.8
9.38    497.    .541    10.121  8.19    20.0    80.8
9.46    541.    .563    8.900   7.81    22.5    97.0
9.53    580.    .587    9.816   7.17    23.8    95.5
9.58    612.    .604    8.923   6.12    17.9    92.2
9.62    663.    .620    8.742   5.21    24.9    97.4
9.65    718.    .644    8.205   4.89    25.0    104.7
9.66    769.    .669    7.114   4.63    20.3    109.3
9.67    848.    .698    6.234   4.26    21.6    115.8
9.71    946.    .736    9.683   3.69    19.7    122.4
9.74    1082.   .787    19.510  3.94    17.4    128.4
9.77    1256.   .887    13.245  4.69    16.9    133.6
9.80    1420.   1.0     9.796   3.73    18.4    123.5
9.82    1624.   1.092   10.626  3.86    19.5    133.3
9.83    1767.   1.169   10.539  3.50    21.0    133.2
9.84    1891.   1.222   9.588   3.17    21.1    135.8


                          FRANCE

POP     PCE     CPI     PW      PS      NDC     TFC

1.      1.      1.      11.957  15.5    1.      1.
46.68   181.3   .440    11.707  16.28   58.7    426.8
46.16   198.4   .451    11.794  15.70   61.1    437.2
47.00   222.3   .474    12.331  15.00   58.4    432.9
47.82   251.8   .499    13.997  14.36   68.0    486.4
48.31   274.7   .514    13.752  13.97   58.6    487.2
48.76   293.7   .528    12.117  13.38   53.8    407.3
49.16   317.9   .542    13.327  11.94   62.2    505.6
49.55   344.0   .557    12.188  10.53   50.2    467.9
49.91   374.5   .582    11.961  8.96    53.5    496.6
50.32   427.0   .618    11.773  8.84    62.9    612.6
50.77   469.1   .654    10.875  8.90    54.2    577.3
51.25   526.0   .690    9.831   8.49    53.4    593.0
51.70   590.8   .733    15.219  7.31    54.0    674.1
52.13   666.2   .787    31.084  7.91    48.7    724.4
52.49   778.4   .895    23.694  9.42    44.5    715.8
52.79   895.0   1.0     16.601  6.97    50.3    697.4
52.92   1034.1  1.092   19.209  7.21    53.0    739.6
53.08   1155.0  1.196   21.098  6.91    51.0    729.1
53.28   1307.3  1.306   20.001  6.96    48.3    765.1


                         GERMANY

POP     PCE     CPI     PW      PS      NDC     TFC

 1        1    1.      10.189   10.47     1       1
55.42   171.8   .575    9.856   10.95   116.9   707.8
56.23   188.3   .588    9.661   10.66   117.1   734.9
56.84   204.8   .606    10.059  10.10   122.7   743.5
57.44   216.8   .624    11.385  9.92    124.1   745.1
58.00   233.5   .638    11.154  10.36   120.1   785.2
58.63   257.6   .659    9.873   10.10   130.8   891.9
59.15   275.1   .682    10.844  8.89    137.5   827.5
59.25   282.6   .693    9.874   7.64    105.2   718.6
59.45   300.8   .705    9.641   6.47    124.3   914.9
60.01   330.8   .718    8.898   5.81    135.5   1011.1
60.71   367.5   .742    7.173   5.08    149.9   996.9
61.29   407.8   .782    6.212   4.67    162.7   1101.4
61.67   447.8   .825    9.620   4.13    169.6   1187.4
61.97   491.7   .882    18.652  4.21    140.6   1176.9
62.04   527.6   .944    12.748  4.72    125.2   1131.2
61.83   576.5   1.0     9.529   3.69    134.9   1181.6
61.51   623.1   1.045   10.120  3.87    143.1   1216.2
61.40   666.6   1.086   9.970   3.41    150.0   1244.2
61.31   709.5   1.114   8.902   3.18    146.1   1304.2


                         HOLLAND

POP     PCE     CPI     PW      PS      NDC     TFC

1.      1.      1.      9.203   9.47    1.      1.
11.48   24.27   .444    9.003   9.96    25.3    137.3
11.64   25.84   .441    8.732   9.23    28.4    149.8
11.80   28.13   .451    9.066   8.76    31.2    152.6
11.97   31.25   .466    10.284  8.39    32.2    165.9
12.12   35.34   .493    10.121  8.19    31.1    173.6
12.29   39.49   .522    8.900   7.81    32.9    173.5
12.45   42.96   .552    9.816   7.17    31.6    182.2
12.60   46.64   .571    8.923   6.12    25.0    169.0
12.72   50.98   .593    8.742   5.21    25.5    172.2
12.87   58.84   .636    8.205   4.89    26.8    184.6
13.03   65.59   .660    7.114   4.63    27.0    195.6
13.19   73.19   .709    6.234   4.26    27.7    202.9
13.33   82.21   .765    9.683   3.69    27.3    200.3
13.44   93.29   .826    19.510  3.94    25.8    196.1
13.54   105.45  .905    13.245  4.69    23.3    192.4
13.65   120.74  1.0     9.796   3.73    23.3    202.0
13.77   136.78  1.088   10.626  3.86    29.7    203.3
13.85   152.36  1.158   10.539  3.50    30.4    209.7
13.94   166.25  1.205   9.588   3.17    30.4    213.0


                          ITALY

POP     PCE     CPI     PW      PS      NDC     TFC

1.      1.      1.      1514.   1826.   1.      1.
49.64   13980.  .397    1482.   1919.   57.3    347.2
49.90   15286.  .405    1493.   1851.   58.4    330.7
50.24   17197.  .424    1562.   1769.   66.7    378.6
51.18   20090.  .456    1775.   1697.   61.1    403.0
51.57   21757.  .483    1752.   1661.   61.8    405.5
51.99   23724.  .504    1545.   1587.   57.1    334.2
52.33   26137.  .516    1694.   1418.   73.2    468.0
52.67   28741.  .535    1546.   1241.   71.5    456.9
52.99   29844.  .543    1506.   1047.   63.9    395.4
53.22   32588.  .557    1420.   991.    72.8    509.3
53.66   37479.  .584    1234.   941.    67.7    553.9
54.01   40836.  .613    1103.   886.    65.4    499.3
54.41   45007.  .648    1760.   714.    72.6    551.8
54.91   53457.  .718    4069.   958.    61.2    718.1
55.41   66464.  .855    3204.   1238.   60.1    606.7
55.83   81446.  1.0     2528.   973.    60.6    533.2
56.17   99504.  1.168   3345.   1176.   62.0    642.0
56.45   120329. 1.366   3789.   1244.   61.7    636.8
56.70   139545. 1.532   3761.   1256.   62.3    660.7 


                          JAPAN

POP     PCE     CPI     PW      PS      NDC     TFC

1.      1.      1.      887.6   1116.   1.      1.
94.10   8823.   .332    859.1   1116.   109.8   690.1
94.95   10106.  .350    868.2   1116.   128.7   704.5
95.83   11747.  .373    907.8   1116.   118.2   738.7
96.81   13769.  .402    1032.4  1109.   123.7   804.6
97.83   16039.  .417    1014.3  947.    116.8   860.7
98.88   18611.  .445    893.6   749.    129.6   1006.9
99.79   21470.  .467    982.7   727.    145.1   999.7
100.83  24743.  .486    897.0   619.    151.3   1160.0
101.96  28627.  .512    870.7   540.    145.3   1241.0
103.17  33212.  .539    811.4   526.    159.9   1239.2
104.34  38647.  .580    704.5   463.    168.7   1403.6
105.69  43559.  .616    620.9   382.    173.2   1456.7
107.18  50267.  .643    914.5   361.    179.9   1477.3
108.70  60489.  .719    1892.8  440.    179.7   1909.3
110.16  73629.  .894    1436.0  538.    173.5   1397.7
111.57  85539.  1.0     1149.5  495.    165.8   1802.5
112.77  96886.  1.093   1191.8  495.    154.8   1530.6
113.86  108115. 1.181   1153.0  460.    151.4   1898.2
114.90  118595. 1.226   932.8   473.    151.0   1998.7



                      UNITED KINGDOM

POP     PCE     CPI     PW      PS      NDC     TFC

1.      1.      1.      .868    .90     1.      1.
52.35   16.94   .368    .85     .95     149.0   766.7
52.81   17.84   .378    .858    .90     150.5   731.1
53.27   18.93   .393    .896    .87     144.8   710.7
53.54   20.13   .401    1.02    .81     146.7   770.9
53.85   21.49   .414    1.005   .73     134.2   848.2
54.18   22.91   .433    .884    .68     124.3   804.9
54.50   24.30   .450    .971    .62     124.5   813.9
54.80   25.49   .462    .907    .57     116.9   786.2
55.05   27.41   .484    1.009   .55     123.6   890.9
55.27   29.15   .510    .947    .53     122.5   813.3
55.42   31.66   .542    .821    .51     114.2   783.4
55.61   35.37   .593    .730    .48     113.7   828.4
55.79   39.89   .636    1.204   .47     120.6   851.5
55.91   45.27   .694    2.846   .54     104.1   930.6
55.93   52.00   .805    2.106   .65     91.8    838.6
55.89   63.38   1.0     1.743   .62     88.2    856.1
55.89   73.46   1.165   2.225   .70     79.2    858.3
55.85   83.58   1.350   2.460   .80     73.3    818.8
55.82   95.74   1.462   2.309   .73     84.3    882.8



                      UNITED STATES 

POP     PCE     CPI     PW      PS      NDC     TFC

1.      1.      1.      3.000   2.80    1.      1.
180.7   324.9   .55     2.949   2.69    260.1   2919.2
183.7   335.0   .556    2.966   2.53    260.6   2880.5
186.5   355.2   .562    3.078   2.32    273.3   3198.3
189.2   374.6   .569    3.418   2.16    269.6   3266.5
191.9   400.4   .576    3.368   1.92    240.5   3399.5
194.3   430.2   .586    3.034   1.70    269.9   3816.6
196.6   464.8   .604    3.274   1.54    253.3   4111.2
198.7   490.4   .620    3.039   1.36    218.7   4019.6
200.7   535.9   .646    2.977   1.05    227.4   4462.6
202.7   579.7   .681    2.826   0.98    209.1   4510.5
204.9   618.8   .721    2.529   0.86    169.5   4316.0
207.1   668.2   .752    2.346   0.80    148.6   4767.9
208.9   733.0   .777    3.579   0.74    141.0   5239.3
210.4   809.9   .826    7.541   0.81    106.8   5325.9
211.9   889.6   .916    5.488   1.03    86.5    4786.4
213.6   979.1   1.0     4.435   1.03    80.4    5145.5
215.4   1089.9  1.058   4.581   1.15    90.2    5906.0
216.8   1210.0  1.127   4.856   1.22    100.1   6314.2
218.6   1350.9  1.212   4.994   1.19    107.9   6691.0


DATA FOR CHAPTER 9

The columns headed OIL, GAS, ELECT. and COAL are 
consumption of those fuels in million therms.  The column 
headed OIL-PRICE, GAS-PRICE, ELECT. and COAL-PRICE are 
the prices in pence per therm, deflated to 1980 prices 
using the consumer price deflator.  AGG-PRICE is the 
composite energy price.  ACTIVITY is consumer expenditure 
in real terms in the domestic sector, industrial 
production in the industrial sector. DEG DAYS is the 
severity of winter.  Fuller definitions and the data 
sources are given in chapter 9.