Separating Inflation and Growth

I am glad to have discovered this 2016 article by Steve Drew, Phil Lewis and Craig McLaren [2],  describing "chain-linking methods used in the U.K. national accounts". I am finally able to clear up some questions that have been bothering me since 2009.  

It is a complex subject, and it may be that they handle the complexities well. But I wish they had written more clearly; their lack of commas, relative pronouns, and examples make their text hard-going for the newcomer. 

        Drew et al. do define their terms, albeit clumsily, and in a jumbled order.

"A current price (CP) estimate records the actual or estimated monetary value for a defined period. The current price estimate is the value expressed in terms of the prices of that period. A time series of CP estimates can be constructed."

(Or, perhaps, put more simply as: "The Current Price estimate of a product is the actual (or estimated) monetary value expressed in terms of the prices of that period. A time series of CP estimates can be constructed."). 

They follow this with a definition of value (which might have been better defined first):

value = volume x price

        For a car factory, volume could be number of cars produced; for a winery, litres of wine. By converting to value the disparate products may be summed. In this way the total productivity of a country can be found year by year, and tabulated in what Drew et al. call 'a time series of Current Price estimates'. (See e.g. Table 1 from [1])

                                Table 1

Year	UK GDP in US$B
1960	73
1961	78
1962	81
1963	87
1964	94
1965	102
1966	109
1967	113
1968	108

However, the question arises, what part of the increase in GDP is real growth, and what part is inflation? If it was just cars or just wine, we could look at the volume figures to see real growth as a factor or  % increase year on year. And, indeed, we could look at the price figures to see inflation in wine price, or inflation in car price. But it is a big job to work out how important wine is to total GDP. 

The method now used in USA, Europe and the UK for GDP, is to tabulate a 'Chained Volume Series' -- thus. 

1. For our year of interest, list every product in the economy with its volume and its price. (We know that the sum of the products of those two quantities give us the GDP.) 
2. List in parallel the data for the previous year.  
3. Instead of multiplying this year's volumes by this year's prices, use the previous year's prices from the adjacent column. 

The GDP so calculated is inflation-proofed, and any increase over the year is due to volume; at least for the 12 month from last year to this.   Why not simply look at volumes? The answer is that we do not know the relative importance of cars and wine, unless we calculate the "values". Or, for another way of seeing this, you cannot sum "wine + cars", only "£ + £". [3]

                                                                        Table 2

Item	Vol. in 2000	Price in 2000	Value in 2000	Vol. in 2001	Price in 2001	Value in 2001	'Volume only GDP' in 2001
Cars	10	100	1,000	10	101	1,010	1,000
Wine	20	1	20	80	1.0	80	80
GDP			1,020			1,090	1, 080

        In Table 2, the right hand column ('Volume-only GDP' in 2001) could be called 'inflation-corrected GDP for 2001. We see that the apparent 6.8%  (1090/1020) increase in 'uncorrected GDP' was partly (1%) due to inflation, and partly (1080/1020 ≣ 5.9%) due to a good wine harvest. 

So far, in this exposition, there is no 'chaining'. So let us look at 2002, or year 2. The question is whether to keep 2000 as base year (year 0) for the next 2 decades, or always use the 'previous year'. The advantage of chaining over indexing to a distant reference year, is explained by the International Monetary Fund [5]: 

"A key recommendation in the 2008 SNA.....is to move away from the traditional national accounts measures “at constant prices”  toward chain-linked measures. Annual chain indices are superior to fixed-base indices, because weights are updated every year to reflect the current economic conditions. Chaining also avoids the need for re-weighting price and volume series when the base year is updated every five or ten years, which usually generates large revisions in the history of price and volume developments." [5]

Table 3, Showing an economy of 3 items through 3 years.

(P0=Prices in year 0, Q= quantity or volume, PxQ =Value in currency units.  C.f. [6].)

	P0	Q0	P0 xQ0	P1	Q1	P1xQ1	P0 xQ1	P2	Q2	P2 xQ2	P0 xQ2	P1 xQ2
Cars	100	10	1000	101	10	1010	1000	102	10	1020	1000	1010
Wine	1.0	20	20	1.0	80	80	80	1.5	20	30	20	20
Paint	1	100	100	2	100	200	100	4	95	380	95	190
GDP 'current'			1120			1290				1430
GDP 'constant'			1120				1180				1115
GDP 'prev. year'							1180					1220

We can see, by comparing P0 with P1, that there is inflation, but we do not know how important the price of paint is to the whole economy.  Uncorrected GDP (shown here as the sum of all the products of P1 x Q1) increase from 1120 to 1290  (which is  a rise of 15%); corrected GDP only rose from 1120 to 1180 (i.e. by +5.4%). It looks like annual inflation of some 10%; growth of 5.4%. (Even though car prices have only gone up 1%, and wine 0%.)

Comparing year 2 with year 1, the uncorrected GDP has risen by a factor of 1430/1290 (i.e. by 1.109 or 10.9% ). But, using P1 prices for both years, we see that GDP corrected for inflation (GDP 'constant p') has fallen 1220/1290, so real GDP fell by a factor of  0.9457, or -5.42%.

Using P0 throughout, we would conclude growth in the first year was from 1120 to 1180 (i.e. growth of 5.36%), and, in the second year, negative growth from 1180 to 1115 (i.e. negative growth of -5.5%) more than cancelling the positive increase the provious year. So, between year 0 and year 2, negative growth 1120 to 1115  (so -0.4%).

Just as we can strip out inflation from real growth by comparing adjacent years using the prices of the earlier year, so we can strip out growth by comparing adjacent years using the quantities from the earlier years (or the later years, or both and take the average) to find an index of pure inflation freed from growth. 

=================

References:

[1]  https://www.macrotrends.net/countries/GBR/united-kingdom/gdp-gross-domestic-product

[2]  https://www.ons.gov.uk/economy/nationalaccounts/uksectoraccounts/methodologies/chainlinkingmethodsusedwithintheuknationalaccounts#chain-linking 

[3]  Note (for the scientifically minded): Volume [in litres] x Price [in GB£ per litre] = Value [in GB£].

[4]  https://researchbriefings.files.parliament.uk/documents/SN04962/SN04962.pdf 

[5]  https://www.imf.org/external/pubs/ft/qna/pdf/2017/chapter8.pdf 

[6]  https://www.dsec.gov.mo/elearning/en/knowledge/124

Suppose car volume remains at 100 but price continues to rise, let us say to £1022/car. 

We could express the value in current (2002) prices as £102,200. 

Or we could express the 2002 value in 2001 prices as £102,200 x 1010/1022=£101,000.

Or we could express it in 2000 prices as £102,200 x 1010/1022 x 1000/1010=£100,000, chaining back to our initial year.