Table 2.12
Contributions to growth for period 3, a sample calculation  The case of volume estimates based on chain fisher formula
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Data  Empty cell  

t0  t1  t2  t3  
Aggregates – current dollars^{1}  Empty cell  
A  80  90  72  48  
B  180  210  240  255  
C  250  450  455  504  
D  100  150  150  135  
AB  260  300  312  303  
CD  350  600  605  639  
Total  610  900  917  942  
Aggregates – price indexes^{2}  Empty cell  
A  100.0  75.0  50.0  25.0  
B  100.0  116.7  125.0  125.0  
C  100.0  150.0  130.0  140.0  
D  100.0  120.0  120.0  100.0  
Aggregates – volume measures (unlinked indexes)^{3}  Empty cell  
AB (Paasche)  100.0  111.1  109.5  109.8  
CD (Paasche)  100.0  121.2  112.0  103.9  
Total (Paasche)  100.0  117.6  111.2  105.7  
AB (Laspeyres)  100.0  115.4  110.7  112.5  
CD (Laspeyres)  100.0  121.4  112.5  104.1  
Total (Laspeyres)  100.0  118.9  111.9  107.0  
AB (Fisher)  100.0  113.2  110.1  111.1  
CD (Fisher)  100.0  121.3  112.3  104.0  
Total (Fisher)  100.0  118.2  111.5  106.3  
Aggregates – volume measures (linked indexes)^{4}  Empty cell  
AB (Fisher)  100.0  113.2  124.6  138.5  
CD (Fisher)  100.0  121.3  136.2  141.7  
Total (Fisher)  100.0  118.2  131.9  140.2  
Aggregates  volume measures (real dollars, reference period = t1) and calculation of contribution to growth  Volume measures  Growth rate  Calculation using the published formula^{5}  Calculation illustrating the weighting^{6}  
t0  t1  t2  t3  (t3 vs t2)  Results in t3  %Δx_{i,t}  W_{1}  W_{2}  Results in t3  
A (C/P * 100)  60.0  90.0  108.0  144.0  33.33%  1.98%  33.33%  0.08  0.76  1.98% 
B (C/P * 100)  210.0  210.0  224.0  238.0  6.25%  1.66%  6.25%  0.26  1.01  1.66% 
C (C/P * 100)  375.0  450.0  525.0  540.0  2.86%  1.49%  2.86%  0.50  1.05  1.49% 
D (C/P * 100)  120.0  150.0  150.0  162.0  8.00%  1.22%  8.00%  0.16  0.93  1.22% 
AB (Fisher)  265.0  300.0  330.2  367.0  11.13%  Empty cell  Empty cell  Empty cell  Empty cell  Empty cell 
CD (Fisher)  494.6  600.0  673.6  700.7  4.02%  Empty cell  Empty cell  Empty cell  Empty cell  Empty cell 
TOTAL (Fisher)  761.1  900.0  1,003.7  1,067.4  6.35%  Empty cell  Empty cell  Empty cell  Empty cell  Empty cell 
Sum of aggregates (A+B+C+D)  Empty cell  Empty cell  Empty cell  Empty cell  Empty cell  6.35%  Empty cell  1.00  3.75  6.35% 
Sum of subaggregates (A+B)  Empty cell  Empty cell  Empty cell  Empty cell  Empty cell  3.64%  Empty cell  0.34  1.77  3.64% 
Sum of subaggregates (C+D)  Empty cell  Empty cell  Empty cell  Empty cell  Empty cell  2.71%  Empty cell  0.66  1.98  2.71% 
1. Series A, B, C, D are the lowest level of aggregation, in current dollars. Series AB and CD are subaggregates while the Total series is the sum of series A, B, C, D. In current dollars, aggregates and subaggregates are perfectly additive for each period. 2. Price indexes at the lowest level of aggregation. These prices take the value 100 in t0. 3. The indexes on the left side are unlinked. They represent growth between two adjacent periods. Paasche and Laspeyres indexes are the basic indexes used to construct the Fisher volume index. The Paasche index is weighted using the relative value (current dollars) of the final period while the Laspeyres index uses the relative value of the initial period. The Fisher index is the geometric mean of the Paasche and Laspeyres indices. 4. Chained indexes represent the growth in volume between the current period and the reference period (t0 in this case). 5. Published formula used to calculate the contribution of each aggregate to total growth
6. The following formula illustrates that the contribution is the growth rate of the aggregate (ΔX) weighted by a factor W. In the case of volume estimates, this factor corresponds to the relative value between the aggregate and the total at period t1 in current dollars, as in the calculation in current dollars. An additional factor of correction (W) is then applied.

Source: Guide to the Income and Expenditure Accounts, Statistics Canada, catalogue no.13017X
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