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European Master in Official Statistics label Index Numbers, National Accounts & Agricultural Economic Statistics: practice questions

European Master in Official Statistics (EMOS) label · European Union · Eurostat and the European Statistical System

Original practice questions written to the published syllabus · not past papers
10worked here, free
21written to this exam in this subject
9syllabus units

About European Master in Official Statistics label

European Master in Official Statistics (EMOS) label is a postgraduate admission exam run by Eurostat and the European Statistical System, for candidates in European Union. Not an exam: a quality label for master's programmes meeting the EMOS curriculum in official statistics.

Official site: ec.europa.eu.

We have not been able to confirm these details against the exam body's own specification, so fees, dates and pass marks are left out on purpose. Check the current format, eligibility, fees and dates on the official site.

Index Numbers, National Accounts & Agricultural Economic Statistics in European Master in Official Statistics label

The 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.

Our 21 European Master in Official Statistics label questions in this subject: 1 easy, 8 medium, 12 hard, across 9 units.

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

These 10 were written to European Master in Official Statistics label and are not shown on any other exam's page.

Question 1 · medium

Two items have base-period expenditure shares of 0.4 and 0.6 and price relatives of 1.10 and 1.30. What is the Laspeyres price index computed as a weighted mean of relatives?

  1. 120.00
  2. 122.00
  3. 121.20
  4. 119.58
Answer and working

B. 122.00

With base expenditure shares as weights, the weighted arithmetic mean of relatives equals the aggregative Laspeyres: 0.4 x 1.10 + 0.6 x 1.30 = 0.44 + 0.78 = 1.22, so 122. 120 is the unweighted mean; 119.58 is the unweighted geometric mean sqrt(1.10 x 1.30) x 100.

Question 2 · hard

Which of these is NOT a superlative index in Diewert's sense?

  1. Laspeyres
  2. Fisher ideal
  3. Tornqvist
  4. Walsh
Answer and working

A. Laspeyres

Superlative indices are exact for flexible functional forms and use symmetric weights from both periods: Fisher, Tornqvist and Walsh. Laspeyres uses base-period weights only and is exact only for a Leontief (no substitution) form.

Question 3 · medium

The value index equals the Laspeyres price index multiplied by which other index?

  1. The Laspeyres quantity index
  2. The Paasche quantity index
  3. The Fisher quantity index
  4. The Paasche price index
Answer and working

B. The Paasche quantity index

sum p1 q0/sum p0 q0 x sum p1 q1/sum p1 q0 = sum p1 q1/sum p0 q0, so L(price) x P(quantity) = V. Laspeyres price times Laspeyres quantity does not cancel; this pairing is why deflating by a Paasche deflator yields a Laspeyres volume index.

Question 4 · hard

Which test does Fisher's ideal index fail?

  1. The time reversal test
  2. The factor reversal test
  3. The circular test
  4. The unit test
Answer and working

C. The circular test

Fisher passes the unit, time reversal and factor reversal tests but not circularity, because its weights change with every pair of periods. No formula satisfies every test at once.

Question 5 · hard

International price comparisons across many countries need transitive results. Which method makes bilateral Fisher indices transitive?

  1. The Carli method, an arithmetic mean of country price ratios
  2. Chaining Laspeyres indices in alphabetical order of countries
  3. The EKS method, a geometric mean through every bridge country
  4. Using each country's own CPI weights in turn as the base
Answer and working

C. The EKS method, a geometric mean through every bridge country

Bilateral Fisher indices fail circularity, so comparisons through different bridge countries disagree. EKS replaces each bilateral Fisher index by the geometric mean of all indirect comparisons through other countries, giving transitive parities. Chaining in an arbitrary order makes results depend on the order.

Question 6 · hard

An industry's output at current prices is 500 and its intermediate consumption 200. The output price index is 125 and the input price index 160 (base = 100). What is real GVA by double deflation?

  1. 240
  2. 275
  3. 300
  4. 187.5
Answer and working

B. 275

Double deflation: real output 500/1.25 = 400, real inputs 200/1.60 = 125, real GVA = 275. Single deflation of nominal GVA 300 by the output index gives 240, understating volume because input prices rose faster than output prices.

Question 7 · medium

Three households have incomes 2, 4 and 6. Using G = Delta / (2 mu), where Delta is the mean absolute difference over all ordered pairs including each with itself, what is the Gini coefficient?

  1. 0.3333
  2. 0.4444
  3. 0.2222
  4. 0.1667
Answer and working

C. 0.2222

Mean = 4. Absolute differences over the 9 ordered pairs sum to 16, so Delta = 16/9 = 1.7778. G = 1.7778/8 = 0.2222. 0.3333 uses only the 6 distinct ordered pairs (16/6/8); 0.4444 forgets the factor 2.

Question 8 · medium

The Lorenz curves of land distribution in two regions cross. What follows?

  1. Different inequality measures may rank them differently
  2. The region with the higher Gini is unambiguously less equal
  3. Both regions must have exactly the same Gini coefficient
  4. Neither region can have a Gini coefficient computed
Answer and working

A. Different inequality measures may rank them differently

Lorenz dominance (one curve wholly above the other) gives an unambiguous ranking for all standard measures; when curves cross, measures sensitive to different parts of the distribution can disagree.

Question 9 · medium

Which inequality measure has an explicit inequality-aversion parameter chosen by the analyst?

  1. The Theil T index
  2. The coefficient of variation
  3. The Atkinson index
  4. The Gini coefficient
Answer and working

C. The Atkinson index

Atkinson's index depends on epsilon, the aversion to inequality: higher epsilon gives more weight to the bottom of the distribution. Theil T, the CV and the Gini have no such parameter.

Question 10 · hard

Four households share all income, but one household holds all of it and the others hold nothing. Using G = Delta / (2 mu) over all ordered pairs, what is the Gini coefficient?

  1. 1.00
  2. 0.75
  3. 0.25
  4. 0.50
Answer and working

B. 0.75

With income 4 held by one household, mu = 1. The 6 ordered pairs involving the rich and a poor household each differ by 4: Delta = 24/16 = 1.5, G = 1.5/2 = 0.75. In general the maximum is (n - 1)/n, approaching 1 only as n grows.

A study plan for Index Numbers, National Accounts & Agricultural Economic Statistics in European Master in Official Statistics label

This plan follows where our questions actually fall, so the time goes where the marks are likely to be. It is our reading of the syllabus, not the exam body's weighting.

  1. First, the heavy units (57% of the 21 questions): Inequality measures: Lorenz curve and Gini coefficient (5, 24%); Index numbers: Laspeyres, Paasche, Fisher and Marshall-Edgeworth (4, 19%); National accounts: GDP, GVA and the System of National Accounts (3, 14%).

    Read the manual chapters for these first and do every worked question you can find on them.

  2. Then the middle band: Tests of index numbers: time reversal, factor reversal and circularity (3, 14%); Index numbers of agricultural production and area (2, 10%); Chain-base indices, base shifting and splicing (1, 5%).

    Aim for one sitting per unit, then mixed questions across them.

  3. Then the lighter units: Growth rates: compound annual growth and trend estimation (1, 5%); Parity index and terms of trade between agriculture and non-agriculture (1, 5%); Wholesale and consumer price indices (1, 5%).

    Learn the definitions, classifications and standard numbers; these units are more often recalled than worked.

  4. Leave time for the hard ones: Chain-base indices, base shifting and splicing (1 hard of 1), Growth rates: compound annual growth and trend estimation (1 hard of 1), Parity index and terms of trade between agriculture and non-agriculture (1 hard of 1).

    Come back to these after a first pass, untimed, and read every explanation, including for the options you rejected.

  5. Bank the easy marks: National accounts: GDP, GVA and the System of National Accounts (1 easy of 3).

    Do these early in revision so they are fast on the day.

  6. Finish timed. Sit the subject as a timed set without notes, mark it, and send each wrong answer back to its unit above.

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