Does a wage rise protect purchasing power? Reading a basket survey against two price indices
A district planning officer in Kangra must report on whether last year's wage revision protected household purchasing power. She has one household-basket survey and two wage series. The basket weights, as percentages of monthly spending, are food 45, fuel 12, rent 8, clothing 10, health 15 and education 10. Over the year the price relatives are: food +9 per cent, fuel +14 per cent, rent +5 per cent, clothing +6 per cent, health +11 per cent and education +8 per cent. The average daily wage in her sample rose from Rs 600 to Rs 653. The state's published consumer price index rose 10.4 per cent over the same period. Her senior wants a one-line conclusion, that wages have risen so purchasing power has improved, and asks her to endorse it. She has no budget for a fresh survey and must also answer a Zila Parishad question about agricultural labourers, whose wages rose only 6 per cent.
1. Compute the basket-based inflation rate and the change in the real wage. Is the senior's one-line conclusion defensible?
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Weighted inflation = sum of (weight x price relative) divided by 100: (45 x 9) + (12 x 14) + (8 x 5) + (10 x 6) + (15 x 11) + (10 x 8) = 405 + 168 + 40 + 60 + 165 + 80 = 918, so 9.18 per cent.
Money wage rose from 600 to 653, that is 53/600 = 8.83 per cent.
Real change = 108.83 / 109.18 = 0.9968, a fall of about 0.32 per cent. Purchasing power did not improve; it fell marginally.
The conclusion is therefore not defensible. But the honest correction is not to swing to 'wages have crashed'. A 0.3 per cent gap is within the noise of a single small survey, so the note should say that money wages rose 8.8 per cent while prices for this basket rose 9.2 per cent, leaving real wages roughly unchanged and slightly negative. That is a different statement from the senior's, and it is the one the arithmetic supports.
2. The Zila Parishad asks about agricultural labourers whose wages rose 6 per cent. What is the answer, and which index should be used?
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Using the same basket, 106 / 109.18 = 0.971, a real fall of about 2.9 per cent. Using the state index of 10.4 per cent, 106 / 110.4 = 0.960, a real fall of about 4.0 per cent. Both point the same way, so the direction of the answer is safe even though the magnitude depends on the index.
The index choice should match the group. Agricultural labourers are best tracked by the consumer price index for agricultural labourers, industrial workers by the index for industrial workers; a general state index blends populations and can misstate either group. The officer should state which index she used, use the same one for wages and prices, and not switch series between the two parts of the report. The answer to the Parishad is that real wages of agricultural labourers fell, by roughly 3 to 4 per cent on these figures.
3. The senior insists on the one-line conclusion. What should the officer do, and what caveats belong in the note?
Read the worked answer
She should decline to certify the sentence and issue a note that states what the numbers show. Endorsing a conclusion that her own arithmetic contradicts turns a routine report into a record that an audit can pull apart, and it also misleads the wage revision that follows.
The note should carry explicit caveats: the weights come from one small survey and have no reported standard error; the wage series and price series may cover different populations; the comparison is over one year, so a base effect can dominate; and the basket may not represent households that buy less food and more health care. The defensible one-liner is that money wages rose 8.8 per cent against basket inflation of 9.2 per cent, leaving real wages roughly flat to slightly negative.
She should also record the disagreement in the file rather than leave the senior's sentence unattributed, and offer the sharper, correct line for the Parishad: agricultural labourers lost real income.