chain-type quantity indexes
uses weights of more than one period, the
These data include a breakdown of GDP into price and quantity indexes
, as well as a GDP implicit price deflator.
The Laspeyres quantity index
uses the prices of the initial period, while the Paasche quantity index
uses the prices of the end period.
The quantity index
was further decomposed into the health status index and the adjusted quantity index
(adjusted for health status).
where the R-element column vectors p and q are respectively the regional price and quantity indexes
, and E is a matrix of independently distributed random errors.
After all, we usually observe values, and the problem is one of obtaining a quantity index
by deflating values with an appropriate price index.
The output price index used here is homogeneous of degree one in prices while the output quantity index
is not necessarily.
The last equation above expresses the growth rate of the continuous-time Divisia quantity index
. The solution to this differential equation is a line integral that is path independent under the maintained assumption of weak separability (Hulten, 1973).
Modifying index numbers for new and disappearing product varieties is one way to implement empirically the recent models of endogenous growth, particularly growth resulting from the expansion of intermediate inputs.(9) Just as new varieties will lower the price indexes, they will raise the quantity index
, reflecting the contribution of new input varieties to productivity.
as the product of the chain-type quantity index
and the 2012
A quantity index
must be employed to evaluate changes in real GDP.