Index Numbers (ECON1320 -L9)

Index Numbers (ECON1320 -L9)

Background on Index Numbers

1. Index numbers

a. Allow relative comparisons of a measure over time (i.e. intertemporal comparisons)

b. Especially useful in comparing changes in the levels of quantity, price or value (i.e. Price * Quantity) over time.

c. Are reported relative to a Base period Index whole value is equal to 100.

d. Measure changes in an individual item for changes in several variables.

Simple Index numbers

1. Price relative

a. Ist =Pt/Ps * 100

Unweighted Aggregate PI

1. Arithmetic Mean of PT (Simple Relative PI)

a. Ist = 1/n * [n ‘sum of’ i=1 (Pit/Pis)] *100

b. Dis. – consider every variables are equally important

2. Ratio of Unweighted Aggregate Prices (Simple Aggregate PI)

a. Ist = [ (n ‘sum of’ i=1 Pit) / (n ‘sum of’ i=1 Pis)] * 100

b. Dis. – each commodity has equal weight. Therefore, this index will be influenced greatly by those unit prices that are very much higher than the other.

Weighted Aggregate PI

1. Laspeyres PI (Fixed weight Index)

a. I (L on the top) st = [n ‘sum of’ i=1 Pit Qis] / [n ‘sum of’ i=1 Pis Qis] * 100

b. Uses the base quantities as weight

c. Measure change in the cost of living

i. Changes between the aggregate cost of base period quantities at current period prices and the aggregate cost of base period quantities at base period prices

d. Dis. – compare to Paasche PI

i. Reasonable if there is not much change in consumption pattern

ii. Unrealistic over time as it makes no allowance for reallocation of budget or technological advance etc.

iii. Might overestimate changes in COL (give large weights on commodities that have become relatively more exp [on the items which are relatively changed more in quantity from base yr])

e. Adv. – Practicable (low cost)

2. Paasche PI

a. I (P on the top) st = (n ‘sum of’ i=1 Pit Qit) / (n ‘sum of’ i=1 Pis Qit) * 100

b. Use period t quantities as weights

c. Measure change in COL

d. Dis. (Compare to Laspeyres)

i. underestimate COL (give large weights to item that are now relative less expensive [on the items which are relatively changed less in quantity from base yr] )

ii. higher cost incurred for data collection

3. Fisher PI

a. Fisher st = square root of (Laspeyres st * Paasche st)

b. Geometric average method

Changes of Base period

a. Irt = Ist / Isr * 100

P/s – the used of 4 corner rule in the changes (or chaining of base period)