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UN Statistical Institute for Asia and the Pacific training Index Numbers, National Accounts & Agricultural Economic Statistics: practice questions

UN Statistical Institute for Asia and the Pacific (SIAP) training · Asia-Pacific · United Nations ESCAP - SIAP

Original practice questions written to the published syllabus · not past papers
10worked here, free
17written to this exam in this subject
9syllabus units

About UN Statistical Institute for Asia and the Pacific training

UN Statistical Institute for Asia and the Pacific (SIAP) training is a professional certification run by United Nations ESCAP - SIAP, for candidates in Asia-Pacific. Courses and e-learning for national statistical office staff; certificates on completion.

Official site: unsiap.or.jp.

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 UN Statistical Institute for Asia and the Pacific training

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 17 UN Statistical Institute for Asia and the Pacific training questions in this subject: 2 easy, 9 medium, 6 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 UN Statistical Institute for Asia and the Pacific training and are not shown on any other exam's page.

Question 1 · medium

Why does a Laspeyres consumer price index tend to overstate the change in the cost of living?

  1. It ignores substitution towards goods whose relative prices fall
  2. It weights prices by the current, not the base, basket of goods
  3. It uses the geometric rather than the arithmetic mean of relatives
  4. It excludes all goods whose prices fall during the period
Answer and working

A. It ignores substitution towards goods whose relative prices fall

A fixed base basket assumes buyers keep the same quantities; in reality they substitute towards relatively cheaper goods, so the fixed basket costs more than the cheapest basket giving the same utility (substitution bias). Using current quantities would be Paasche, which understates.

Question 2 · medium

Which index satisfies the circular test?

  1. The simple geometric mean of price relatives
  2. The Fisher ideal index
  3. The Laspeyres index with changing base weights
  4. The Paasche index
Answer and working

A. The simple geometric mean of price relatives

The geometric mean of relatives is transitive: GM(p1/p0) x GM(p2/p1) = GM(p2/p0). Fixed-weight aggregative indices also pass. Fisher, Laspeyres and Paasche change weights with the comparison and fail circularity.

Question 3 · medium

The Carli elementary index (arithmetic mean of price relatives) is avoided in many CPIs mainly because it

  1. Fails the unit test when items are heterogeneous
  2. Cannot be computed when any price falls
  3. Fails time reversal and has an upward bias
  4. Requires current-period quantity data
Answer and working

C. Fails time reversal and has an upward bias

The arithmetic mean of relatives forward and the arithmetic mean of reverse relatives multiply to more than one, so Carli drifts upwards, especially when chained. The unit-test failure belongs to Dutot with heterogeneous items; Carli needs no quantities.

Question 4 · hard

Two items both cost 10 in period 0. In period 1 one costs 15 and the other 5; in period 2 both cost 10 again. What is the chained Carli index for period 2 (period 0 = 100)?

  1. 100.00
  2. 83.33
  3. 133.33
  4. 150.00
Answer and working

C. 133.33

Link 1 = (1.5 + 0.5)/2 = 1.00; link 2 = (10/15 + 10/5)/2 = (0.6667 + 2)/2 = 1.3333. Chained = 133.33, although prices are back where they started: this is chain drift. A chained Jevons index would give exactly 100.00 here, since sqrt(1.5 x 0.5) x sqrt(0.667 x 2) = 1.

Question 5 · medium

Why does the international CPI manual favour the Jevons formula for elementary aggregates?

  1. It is the only formula that needs no price data
  2. It gives each item a weight proportional to its price
  3. It passes time reversal and allows for some substitution
  4. It always gives a higher index than the Carli formula
Answer and working

C. It passes time reversal and allows for some substitution

Jevons, the geometric mean of relatives, is time-reversible and transitive and is consistent with some substitution within the aggregate. Weighting by price level describes Dutot, and Jevons is never above Carli.

Question 6 · medium

FAO's agricultural production indices value each commodity at which prices to aggregate across commodities and countries?

  1. Each country's current retail consumer prices
  2. International commodity prices of a base period
  3. Each country's export prices in national currency
  4. Prices of the year with the highest world output
Answer and working

B. International commodity prices of a base period

Using the same international base-period prices for all countries puts commodities into a common unit and makes country indices comparable. National prices would differ between countries.

Question 7 · easy

The System of National Accounts 2008 was issued jointly by which organisations?

  1. FAO, WHO, ILO, UNESCO and the World Trade Organization
  2. UN, FAO, IFAD, the World Food Programme and OECD
  3. UN, IMF, World Bank, OECD and European Commission
  4. IMF, Bank for International Settlements and regional banks
Answer and working

C. UN, IMF, World Bank, OECD and European Commission

The SNA is the joint international standard of the United Nations, IMF, World Bank, OECD and European Commission (Eurostat); the 2025 update was adopted by the UN Statistical Commission.

Question 8 · medium

Under the SNA, crops grown and consumed by the farm household itself are

  1. Excluded because they never pass through a market
  2. Included only if they exceed half of the harvest
  3. Recorded as intermediate consumption of households
  4. Included in output and valued at producer prices
Answer and working

D. Included in output and valued at producer prices

The SNA production boundary includes all production of goods for own final use; subsistence crops are output, valued at prices of similar goods sold on markets. Excluding them would understate agriculture badly where subsistence farming is common.

Question 9 · hard

Residuals of a semi-log trend fitted to annual crop output are positively autocorrelated. What is the usual consequence for ordinary least squares?

  1. The growth estimate becomes biased upwards in all samples
  2. The standard error of growth is overstated, tests too strict
  3. The coefficient of determination is forced to zero
  4. Standard error of growth understated, so tests too liberal
Answer and working

D. Standard error of growth understated, so tests too liberal

With positive autocorrelation the OLS slope stays unbiased but its usual standard error is too small, so significance is overstated. Remedies include generalised least squares or autocorrelation-robust standard errors.

Question 10 · hard

For two people with incomes 1 and 3, Theil's T index is 0.1308. What is Theil's T for two people with incomes 2 and 6?

  1. 0.2616
  2. 0.0654
  3. 0.8240
  4. 0.1308
Answer and working

D. 0.1308

Theil's T is scale invariant: doubling every income leaves y_i/mu unchanged, so T stays 0.1308. Check: mu = 4, T = 0.5 x (0.5 ln 0.5 + 1.5 ln 1.5) = 0.1308. Doubling it confuses T with the variance, which is not scale invariant.

A study plan for Index Numbers, National Accounts & Agricultural Economic Statistics in UN Statistical Institute for Asia and the Pacific training

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 (47% of the 17 questions): Inequality measures: Lorenz curve and Gini coefficient (3, 18%); National accounts: GDP, GVA and the System of National Accounts (3, 18%); Chain-base indices, base shifting and splicing (2, 12%).

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

  2. Then the middle band: Index numbers: Laspeyres, Paasche, Fisher and Marshall-Edgeworth (2, 12%); Tests of index numbers: time reversal, factor reversal and circularity (2, 12%); Wholesale and consumer price indices (2, 12%).

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

  3. Then the lighter units: Estimation of agricultural GVA and value of output (1, 6%); Growth rates: compound annual growth and trend estimation (1, 6%); Index numbers of agricultural production and area (1, 6%).

    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 (2 hard of 2), Growth rates: compound annual growth and trend estimation (1 hard of 1), Index numbers: Laspeyres, Paasche, Fisher and Marshall-Edgeworth (1 hard of 2).

    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 (2 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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