Chained calculation

In the context of price indices, a chained calculation or chain system means a calculation is done one increment at a time and then multiplied to produce the index for the target date. The increment is usually a year. A chained calculation is in contrast to a fixed-base calculation that calculates the target in one shot. In this sense a chained calculation is "path-dependent".

The chained version of an index may require more data points in order to calculate the index for all years. To give an example, the fixed-base version of the Laspeyres index does not require quantity data for all years (only for the base year), even to calculate the index for all years [1]. In contrast, the chained version requires quantity data for all years.

History

Chain calculations were introduced in the economics literature independently by Lehr (1885) and Marshall (1887).Template:Rp

When to use or avoid chained calculations

"The main advantage of the chain system is that under normal conditions, chaining will reduce the spread between the Paasche and Laspeyres indexes"Template:Rp

"one should chain if the prices and quantities pertaining to adjacent periods are more similar than the prices and quantities of more distant periods, since this strategy will lead to a narrowing of the spread between the Paasche and Laspeyres indices at each link."Template:Rp

Devec database

Some data in the devec database use chained values. From the MySQL prompt:

select metric,units
from data where region = 'Japan' and (metric REGEXP 'chain' or units REGEXP 'chain')
group by metric,units;

(The region = 'Japan' is just to make the query run faster as region is an indexed column.)

This returns:

+----------------------------------------------------------------------+---------------------------------+
| metric                                                               | units                           |
+----------------------------------------------------------------------+---------------------------------+
| Chain-index: Real gross domestic product                             | ?                               |
| Expenditure-side real GDP at chained PPPs                            | 2005 international dollar       |
| Expenditure-side real GDP at chained PPPs                            | 2011 international dollar       |
| growth rate of Real GDP Chain per capita (RGDPCH)                    | Unitless                        |
| Output-side real GDP at chained PPPs                                 | 2005 international dollar       |
| Output-side real GDP at chained PPPs                                 | 2011 international dollar       |
| PPP Converted GDP Chain per equivalent adult at 2005 constant prices | 2005 international dollar       |
| PPP Converted GDP Chain per worker at 2005 constant prices           | 2005 international dollar       |
| PPP Converted GDP Per Capita (Chain Series), at 2005 constant prices | 2005 international dollar       |
| Real GDP Chain per equivalent adult                                  | international dollar per person |
| Real GDP chain per worker                                            | ? per person                    |
| Real GDP Chain per worker                                            | international dollar per person |
| Real GDP per capita (Constant Prices: Chain series)                  | international dollar            |
+----------------------------------------------------------------------+---------------------------------+
13 rows in set (0.38 sec)

External links

• Price index § Chained vs non-chained calculations
• Chained dollars
• United States Chained Consumer Price Index (related or a different meaning of "chained"?)