Worked example 6 — Double counting, and the value added method that cures it

Marshall's definition of national income — the labour and capital of a country acting on its natural resources produce annually a certain net aggregate of commodities, material and immaterial including services of all kinds, and this is the true net annual income or revenue of the country, or national dividend — has three recognised defects. The second is the one that generates arithmetic:

Double counting. A commodity or service may be counted twice or more.

A peasant sells wheat worth Rs. 2,000 to a flour mill; the mill sells flour to a wholesaler; the wholesaler sells to a retailer; the retailer sells to customers. Counting each transaction gives Rs. 8,000, when in actuality the increase in national income is only Rs. 2,000.

Notice what the figure Rs. 8,000 is: it is the sum of four sale values, each of which contains inside it the value of everything bought earlier in the chain. The wheat is counted four times over — once when the peasant sells it, again inside the price of the flour, again inside the wholesaler's price, again inside the retailer's price.

Cure 1 — count only final products. The first rule governing what enters Gross National Product is that only final products are counted, precisely to avoid double counting. On the illustration, count only the retailer's sale to customers.

The difficulty is practical rather than logical: a statistician looking at a firm's books cannot always tell whether a sale is final or intermediate. Flour sold to a household is final; the identical sack sold to a bakery is intermediate.

Cure 2 — the expenditure method. Add up what final buyers spent: consumer expenditure on services and on durable and non-durable goods (C); investment in fixed capital, including residential and non-residential building, machinery and inventories (I); Government expenditure on final goods and services (G); exports (X), less imports (M). Hence GDP at market prices = C + I + G + (X – M), where net exports may be positive or negative. Only final purchases appear, so double counting cannot arise — but the method needs data on buyers, not on producers.

Cure 3 — the value added method, which is the one that scales. Instead of asking which sales are final, ask what each producer added. Subtract from each firm's sales the value of what it bought in.

The intermediate values below are constructed for this example, so that the chain sums correctly to the totals of Rs. 8,000 gross and Rs. 2,000 net. They are illustrative arithmetic, not data.

Let the four sale values run 2,000 → 2,000 → 2,000 → 2,000, which is the arithmetic that produces the Rs. 8,000 from a Rs. 2,000 contribution: each stage sells at the same value and adds nothing but its own margin, which in this stripped illustration is zero at every stage after the first.

| Stage | Sells for | Bought in | Value added | |---|---|---|---| | Peasant | 2,000 | 0 | 2,000 | | Flour mill | 2,000 | 2,000 | 0 | | Wholesaler | 2,000 | 2,000 | 0 | | Retailer | 2,000 | 2,000 | 0 | | Total sales 8,000 | | | Total value added 2,000 |

The gross figure and the value added figure are both correct answers to different questions. Rs. 8,000 is the turnover generated in the economy; Rs. 2,000 is the addition to national income. Only the second is national income, because the other Rs. 6,000 is the same wheat being handed along.

The general identity: value added = sales less purchases of intermediate goods and services, summed over all producers. This is why the product method of measuring GDP is described as the sum of gross value added.

The Ministry of Statistics and Programme Implementation states it exactly this way. Gross Value Added is the total value of goods and services produced in the country after subtracting the cost of raw materials and inputs used to produce them. It is a measure of the contribution to GDP made by an individual producer, industry or sector.

And the relation between the two aggregates is arithmetical: GDP is arrived at by summing all the GVAs and adding taxes on products and subtracting subsidies on products — the last expression often stated together as net taxes on products.

So:

GDP = Σ GVA + taxes on products – subsidies on products

Why the two series are published together. GVA measures production from the producer's side, before the tax wedge; GDP measures it from the buyer's side, after it. If a Government raises indirect taxes, GDP can rise while GVA does not — which is why analysts read GVA when they want to see what the economy actually produced. That is a point of real examination value, because it is the honest answer to a question about whether a rise in GDP means the economy produced more.

Double counting is only the first of the exclusions.

1. Only final products — the rule this example is about.
2. Goods and services rendered free of charge are excluded, because their market price cannot be correctly estimated: a mother bringing up a child, a teacher instructing his own son, a musician playing for friends.
3. Transactions not arising from the produce of the current year are excluded — sale and purchase of old goods, and of shares, bonds and assets of existing companies, because these add nothing to the national product and merely transfer goods.
4. Transfer payments are excluded — unemployment insurance allowance, old age pension, interest on public loans — because the recipients provide no service in return.
5. Capital gains and losses from mere price fluctuation are excluded. If the price of a house rises with inflation the profit on selling it is not part of GNP; but if a portion of the house is newly constructed this year, that addition is included.
6. Income earned through illegal activities is excluded, though black-market goods are priced and meet people's needs.
7. GNP is measured in money at current prices, so it must be adjusted to a base year to give GNP at constant prices.

Rule 2 produces the famous Pigou paradox: Pigou confined national income to that part of the objective income of the community, including income derived from abroad, which can be measured in money — with the consequence that a woman's services as a nurse are included while the same work done unpaid at home is not.

Rule 3 is the one students most often get wrong in an examination. Buying a share of an existing company adds nothing to national product; it transfers a claim.

Marshall's other two defects survive value added accounting and should be named in any answer:

• Goods and services produced are so varied and numerous that a correct estimate is very difficult.
• Many commodities are never marketed — the producer keeps the produce for self-consumption or barters it, which happens constantly in an agriculture-oriented country like India — so national income is underestimated.

The second matters more in India than in a fully monetised economy, and it connects directly to Module 2: a country in which agriculture accounts for nearly one-fifth of national income at current prices but 46.1 per cent of the workforce has a very large volume of production that never passes through a market at all.

The stage-by-stage figures in step 3 are constructed to reproduce the Rs. 8,000 and Rs. 2,000 and are illustrative arithmetic, not data. The GVA and GDP definitions, the seven GNP rules, and the Marshall, Pigou and Fisher definitions may be quoted.

1. Double counting: four sales of the same Rs. 2,000 of wheat give Rs. 8,000 of turnover but only Rs. 2,000 of national income.
2. Three cures: count only final products; use the expenditure method, C + I + G + (X – M); or use value added — sales less intermediate purchases, which is the method that scales.
3. GVA = output less the cost of raw materials and inputs. GDP = ΣGVA + taxes on products – subsidies on products. GVA is before the tax wedge; GDP after it.
4. Also excluded from GNP: free services, old goods and existing securities, transfer payments, capital gains from price change, illegal income. GNP must be rebased to constant prices.
5. Two defects value added does not cure: the sheer variety of output, and unmarketed production — which is large in an agriculture-oriented economy.