Indian Statistical Service Examination (with Indian Economic Service) · India · Union Public Service Commission
Original practice questions written to the published syllabus · not past papersThe measures national statisticians compile: index-number theory and tests, wholesale and consumer price indices, agricultural production and parity indices, terms of trade, and national accounts with agriculture's gross value added. Business-statistics treatments of index numbers are in the Agribusiness track; this goes to compilation level.
In the exams: UPSC ISS Statistics IV (heavy, reported); SSC CGL JSO (heavy); RBI Grade B DSIM (present); state statistical-officer exams (heavy)
How our questions for Indian Statistical Service Examination spread across the units of Index Numbers, National Accounts & Agricultural Economic Statistics. Difficulty: 24 easy, 30 medium, 4 hard.
| Index numbers: Laspeyres, Paasche, Fisher and Marshall-Edgeworth | 9 | |
| Chain-base indices, base shifting and splicing | 9 | |
| Wholesale and consumer price indices | 9 | |
| Tests of index numbers: time reversal, factor reversal and circularity | 7 | |
| National accounts: GDP, GVA and the System of National Accounts | 7 | |
| Growth rates: compound annual growth and trend estimation | 6 | |
| Parity index and terms of trade between agriculture and non-agriculture | 5 | |
| Inequality measures: Lorenz curve and Gini coefficient | 4 | |
| Estimation of agricultural GVA and value of output | 2 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A Laspeyres price index is 125 and the Paasche price index for the same data is 116. What is Fisher's ideal index?
B. 120.42
Fisher = sqrt(L x P) = sqrt(125 x 116) = sqrt(14500) = 120.42. 120.50 is the arithmetic mean (Dorbish-Bowley), which is always at least the geometric mean; 241 is the sum, and 9 the difference.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
A value index between periods 0 and 1 is defined as
B. sum p1 q1 / sum p0 q0 x 100
A value index compares total expenditure, so both prices and quantities change. sum p1 q0 / sum p0 q0 is the Laspeyres price index, sum p1 q1 / sum p0 q1 the Paasche price index and sum q1 p0 / sum q0 p0 the Laspeyres quantity index.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
Which formula satisfies both the time reversal and the factor reversal tests?
C. Fisher ideal index
Fisher's index sqrt(L x P) passes both, which is why Fisher called it ideal. Marshall-Edgeworth passes time reversal only; Laspeyres and Paasche fail both.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
An old price series stood at 180 in the overlap year, when the new series began at 100. The new series is 115 two years later. What is that value expressed on the old base?
B. 207.00
Splicing factor = 180/100 = 1.80, so 115 x 1.80 = 207. 195 adds 15 points to 180; 63.89 divides 115 by 1.80, converting the wrong way.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
A farm wage rises by 12% in a year in which the consumer price index rises by 5%. What is the growth of the real wage?
D. 6.67%
Real growth = 1.12/1.05 - 1 = 6.67%. 7.00% is the subtraction approximation, close but not exact; 17.60% compounds the two instead of deflating.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
A producer price index measures the prices received by domestic producers
C. Excluding taxes on products
A PPI uses basic prices, the amount the producer receives, excluding taxes on products and including subsidies on products; it fits the national accounts concept of output. Retail prices with margins and taxes are what the CPI measures.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
Core inflation is usually computed by excluding which components from the CPI?
B. Food and energy
Core inflation removes the volatile food and energy components (or trims extreme price changes) to show underlying inflation. Housing, health and clothing are kept.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
Which of these is NOT one of the institutional sectors of the SNA?
D. Agriculture, forestry and fishing
SNA institutional sectors are non-financial corporations, financial corporations, general government, households and NPISHs. Agriculture, forestry and fishing is an industry (a classification of activities), not an institutional sector.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
Agricultural output rises from 200 to 300 over six years. What is the compound annual growth rate?
C. 6.99%
CAGR = (300/200)^(1/6) - 1 = 1.5^(0.1667) - 1 = 6.99%. 8.33% is the simple average 50%/6; 50% is the total change.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
The main weakness of a point-to-point compound growth rate is that it
C. Depends heavily on the two end-point years
It uses only the first and last observations, so a drought or bumper year at either end distorts it. Triennium averages at the ends or a fitted trend reduce this.
Further reading: Consumer Price Index Manual (IMF and partners, 2020); System of National Accounts 2008; Goon, Gupta and Dasgupta, Fundamentals of Statistics Vol. 2; Cowell, Measuring Inequality
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