Could anyone suggest me how to construct a price index for an output series when the data are available on both current price as well as constant price for output series?
Suppose x is the series in current prices and y the series in constant prices. Then
p = x / y
where p is the price index. You might multiply p by 100, if you want to have the price index equal to 100 in the base year
ISSUE: Price Index
INDEX: Altogether there are 9 different commonly employed indices depending on the intended use and the nature of the data. These indices include:
1. Bowley index
2. Fisher index
3. Geometric mean index
4. Harmonic mean index
5. Lapeyres index
6. Marshal-Edgeworth index
7. Mitchell index
8. Paarsche index
9. Walsh index
All indices have one thing in common: (i) price and quantity at the initial period, and (ii) price and quantity at the current period.
INDEX SELECTION: The following 7 indices may be relevant: Bowley index, Fisher index, Lapreyes, and Paasche’s index. The Bowley index dependends on Lapreyes index and Paasche’s index. The Bowley index equation is given by:
(1) PB = (PL + PP) / 2
… where PL = Lapreyes’ index and PP is the Paasche’s index. The Lapreyes’ index is given by:
(2) PL = Σ(PnQ0) / Σ(P0Q0)
… where Pn = price at nth period, Q0 = quantity at initial period.
The paasche’s index is given by:
(3) PP = Σ(PnQn) / Σ(P0Qn)
… where Pn = price at nth period; Qn = quantity at nth period; P0 = price at initial period; and Q0 = quantity at initial period.
Lastly, the Fisher index is given by:
(4) PF = sqrt[(PL)(PP)]
… where PL = Lapreyes’ index defined above, and PP = Paasche’ index defined above.
The geometric mean and harmonic mean indices may be appropriate for special scenarios. The other remaining three: Marshall-Edgeworth, Mitchell and Walsh may be given as follows:
Marshall-Edgeworth Index:
(5) PME = Σ(pn(q0 + qn)) / (v0 + vn)
… where vn = (pnqn)
Mitchell Index:
(6) PM = Σ[pn(qa)] / Σ(P0(qa))
Walsh Index:
(7) PW = ([Σ(sqrt(q0qn)]pn) / ([Σ(sqrt(q0qn)]p0)
REFERENCES:
[1] Fisher, I. The Making of Index Numbers: A Study of Their Varieties, Tests and Reliability, 3rd ed. New York: Augustus M. Kelly, 1967.
[2] Kenney, J. F. and Keeping, E. S. "Index Numbers." Ch. 5 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 64-74, 1962.
[3] Mudgett, B. D. Index Numbers. New York: Wiley, 1951.
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